[{"id": "ejde-10", "words": "8775", "extension": ".pdf", "flesch": "75", "author": "Ichida, Yu", "title": "Traveling waves with singularities in a damped hyperbolic MEMS type equation in the presence of negative powers nonlinearity", "date": "2023", "keywords": "dynamics; equation; \u03b52c2; \u03c6(\u03be", "summary": "In addition, the asymptotic behaviors are \u03c6(\u03be) \u223c C(\u03be+ \u2212 \u03be) 2 \u03b1+1 \u03c8(\u03be) \u223c \u2212C (\u03be+ \u2212 \u03be)\u2212 \u03b1\u22121 \u03b1+1 (2.3) as \u03be \u2192 \u03be+ \u2212 0, and \u03c6(\u03be) \u223c C(\u03be \u2212 \u03be\u2212) 2 \u03b1+1 \u03c8(\u03be) \u223c C (\u03be \u2212 \u03be\u2212) \u2212\u03b1\u22121 \u03b1+1 (2.4) as \u03be \u2192 \u03be\u2212 + 0, with C > 0. In addition, the quenching rates are \u03c6(\u03be) \u223c \u2212C(\u03be+ \u2212 \u03be) 2 \u03b1+1 \u03c8(\u03be) \u223c C (\u03be+ \u2212 \u03be)\u2212 \u03b1\u22121 \u03b1+1 (2.1) as \u03be \u2192 \u03be+ \u2212 0, and \u03c6(\u03be) \u223c \u2212C(\u03be \u2212 \u03be\u2212) 2 \u03b1+1 \u03c8(\u03be) \u223c \u2212C (\u03be \u2212 \u03be\u2212) \u2212\u03b1\u22121 \u03b1+1 (2.2) as \u03be \u2192 \u03be\u2212 + 0, with C > 0.", "mime": "application/pdf"}, {"id": "ejde-100", "words": "5751", "extension": ".pdf", "flesch": "77", "author": "Gharehgazlouei, Fariba; Graef, John R.; Heidarkhani, Shapour; Kong, Lingju", "title": "Existence and multiplicity of solutions to a fractional p-Laplacian elliptic Dirichlet problem", "date": "2023", "keywords": "+1 n", "summary": "Introduction In this article, we examine the nonlinear elliptic equation involving the fractional p-Laplacian and depending on a real parameter \u03bb > 0, (\u2212\u2206)spu = \u03bbf(x, u) + h(u), in \u2126, u = 0, on RN\\\u2126, (1.1) where sp < N , \u2126 is a bounded open subset of RN with a Lipschitz boundary, the fractional p-Laplacian operator (\u2212\u2206)sp is defined by (\u2212\u2206)spu(x) = 2 lim \u03b5\u21980 \u222b RN\\B\u03b5(x) Here, |\u2126| is the Lebesgue measure of \u2126, \u03c9N denotes the volume of the N -dimensional unit ball, and W\u0303 s,p(RN ) is the space of all u \u2208 Xp s (\u2126) such that u\u0303 \u2208W s,p(RN ), where u\u0303 is the extension by zero of u. Remark 2.2.", "mime": "application/pdf"}, {"id": "ejde-1009", "words": "7763", "extension": ".pdf", "flesch": "67", "author": "Llibre, Jaume; Zhao, Yulin", "title": "Final evolutions for Lotka-Volterra systems in R^3 having a Darboux invariant", "date": "2025", "keywords": "invariant; lotka; phase; poincare\u0301; singular; system; volterra", "summary": "For this class of Lotka-Volterra systems we can describe completely their phase portraits in the Poincare\u0301 ball. For more details on Lotka-Volterra systems see for instance", "mime": "application/pdf"}, {"id": "ejde-101", "words": "8814", "extension": ".pdf", "flesch": "79", "author": "Liu, Kui; Feckan, Michal; O'Regan, Donal; Wang, Jinrong", "title": "(omega, c)-periodic solutions for non-instantaneous impulsive systems with unbounded time-varying coefficients", "date": "2022", "keywords": "j=1; s(t; s(\u03c9; solutions", "summary": "= Bi(ti)y(t\u2212i ), i \u2208 N+, y(t) = Bi(t)y(t\u2212i ), t \u2208 (ti, si], i \u2208 N+, y(s+ i ) + bi, i \u2208 N+, y(t) = Bi(t)y(t\u2212i ) + bi, t \u2208 (ti, si], i \u2208 N+, y(s+ i )", "mime": "application/pdf"}, {"id": "ejde-102", "words": "4954", "extension": ".pdf", "flesch": "84", "author": "Zhou, Jundong", "title": "k-Hessian curvature type equations in space forms", "date": "2022", "keywords": "h11", "summary": "(3.24) Applying (2.8) and (3.9), we obtain F ii\u2207iih11 = F ii\u220711hii \u2212 h11F iih2 ii + F iihiih 2 11 \u2212KF ii(h11\u03b4 2 1i \u2212 h11\u03b4ii + hii \u2212 hi1\u03b4i1) = F ii\u220711hii \u2212 h11F iih2 ii + f\u0303h2 11 +Kh11 \u2211 i F ii \u2212 f\u0303K. (3.25) Covariantly differentiating (3.11) twice yields F ii\u220711hii = Gii\u220711\u03b7ii \u2265 \u2212Gij,rs\u22071\u03b7ij\u22071\u03b7rs+ \u2211 i h11id\u03bd We prove that a 2(u\u2212 a) F iih2 ii + 1 2 (K + \u03b2\u03c6\u2032) \u2211 i F ii \u2265 C2h11.", "mime": "application/pdf"}, {"id": "ejde-1036", "words": "8055", "extension": ".pdf", "flesch": "83", "author": "Lan, Kunquan", "title": "Existence and uniqueness of generalized normal solutions to first order fractional differential equations and applications", "date": "2024", "keywords": "c([a; fractional", "summary": "Let C([a, b]; J) = {u \u2208 C[a, b] : u(x) \u2208 J for each x \u2208 [a, b]}. If J = [c, d], then u(x) \u2208 J for each x \u2208 [a, b].", "mime": "application/pdf"}, {"id": "ejde-1037", "words": "6150", "extension": ".pdf", "flesch": "89", "author": "Freitas, Mirelson M.; Santos, Mauro L.; Raposo, Carlos A.; Ramos, Anderson A.; Ferreira, Jorge", "title": "Blow-up solutions for damped Rao-Nakra beams with source terms", "date": "2025", "keywords": "nakra; rao", "summary": "[16], \u03c11h1utt \u2212 E1h1uxx \u2212 \u03c4 = 0, (1.4) \u03c13h3vtt \u2212 E1I1\u03d51,xx \u2212 h1 2 \u03c4 +G1h1(wx + \u03d51)", "mime": "application/pdf"}, {"id": "ejde-104", "words": "9611", "extension": ".pdf", "flesch": "79", "author": "Barreira, Luis; Valls, Claudia", "title": "Some applications of Lyapunov regularity", "date": "2022", "keywords": "lim; log; lyapunov; sequence", "summary": ", q let \u03b1i = lim inf m\u2192+\u221e 1 m log m\u220f l=1 |alii| and \u03b1i = lim sup m\u2192+\u221e 1 m log m\u220f l=1 |alii|. , q let \u03b1i = lim inf m\u2192+\u221e 1 m log m\u220f l=1 |alii| and \u03b1i = lim sup m\u2192+\u221e 1 m log m\u220f l=1 |alii|. (3.1)", "mime": "application/pdf"}, {"id": "ejde-105", "words": "8722", "extension": ".pdf", "flesch": "81", "author": "Kishimoto, Nobu", "title": "Remarks on periodic Zakharov systems", "date": "2022", "keywords": "c([0; case; solution; uniqueness", "summary": "Let u \u2208 C([0, T\u221e);H1) be the (forward-in-time) maximal-lifespan solution of i\u2202tu+ \u2206u = \u2212 ( |u|2 \u2212 Pc(|u|2)\u2212 \u03bd0 \u2212 \u03bd1t ) u, t \u2208 (0, T\u221e), x \u2208 Td\u03bb, u \u2223\u2223 t=0 = u\u221e0 . By the Ho\u0308lder inequality, the Sobolev embedding, interpolation and the Duhamel formula, we see that, for t \u2208", "mime": "application/pdf"}, {"id": "ejde-1051", "words": "7365", "extension": ".pdf", "flesch": "82", "author": "Wu, Chun", "title": "Global boundedness in an indirect chemotaxis-consumption model with signal-dependent degenerate diffusion", "date": "2025", "keywords": "chemotaxis; tmax; \u222b \u03c9", "summary": "Using wq\u22121 to test the third equation of (1.6) and integrating gives 1 q d dt \u222b \u2126 wq = \u2212\u03b4 \u222b \u2126 wq + \u222b \u2126 uwq\u22121 \u2264 \u2212\u03b4 \u222b \u2126 wq + \u03b4 2 \u222b \u2126 wq + C \u222b \u2126 uq (2.6) for all t \u2208 (0, Tmax) which implies (2.5) with (2.3) and Lemma 2.4. \u25a1 Lemma 2.7. Applying integration by parts to the second equation in (1.6) and using the well-known equation 2\u2207v \u00b7 \u2207\u2206v = \u2206|\u2207v|2 \u2212 2|D2v|2, we find that d dt \u222b \u2126 v1\u2212p|\u2207v|p = p \u222b \u2126 v1\u2212p|\u2207v|p\u22122\u2207v \u00b7 \u2207(\u2206v \u2212 uvw)\u2212 (p\u2212 1) \u222b \u2126 v\u2212p|\u2207v|p(\u2206v \u2212 uvw) = p 2 \u222b \u2126 v1\u2212p|\u2207v|p\u22122(\u2206|\u2207v|2 \u2212 2|D2v|2)\u2212 p \u222b \u2126 v1\u2212p|\u2207v|p\u22122\u2207v \u00b7 \u2207(uvw) \u2212 (p\u2212 1) \u222b \u2126 v\u2212p|\u2207v|p\u2206v + (p\u2212 1) \u222b \u2126 wv1\u2212p|\u2207v|p = p(p\u2212 1) \u222b \u2126 v\u2212p|\u2207v|p\u22122\u2207v \u00b7 \u2207|\u2207v|2 \u2212 p \u222b \u2126 v1\u2212p|\u2207v|p\u22122|D2v|2 \u2212 p(p\u2212 2) 4 \u222b \u2126 v1\u2212p|\u2207v|p\u22124|\u2207|\u2207v|2|2 \u2212 p(p\u2212 1) \u222b \u2126 v\u2212p\u22121|\u2207v|p+2 + p 2 \u222b \u2202\u2126 v1\u2212p|\u2207v|p\u22122 \u00b7 \u2202|\u2207v|2 \u2202\u03bd + p(p\u2212 2) 2 \u222b \u2126 wv\u2212p+2|\u2207v|p\u22124\u2207v \u00b7 \u2207|\u2207v|2 + p \u222b \u2126 wv\u2212p+2|\u2207v|p\u22122\u2206v \u2212 (p\u2212 1)2 \u222b \u2126 wv1\u2212p|\u2207v|p. (3.5) EJDE-2025/09 CHEMOTAXIS-CONSUMPTION MODEL 9 The pointwise identity [49, Lemma 3.2] and \u2207|\u2207v|2 = 2D2v \u00b7 \u2207v imply that p(p\u2212 1) \u222b \u2126 v\u2212p|\u2207v|p\u22122\u2207v \u00b7", "mime": "application/pdf"}, {"id": "ejde-106", "words": "8490", "extension": ".pdf", "flesch": "87", "author": "Millla Miranda, Manuel; Louredo, Aldo Trajano; Clark, Marcondes Rodrigues; Gouveia, Giovana Siracusa", "title": "Nonstationary Lame system without definite sign energy", "date": "2022", "keywords": "div; i=1", "summary": "(4.6) Putting the above two expressions in (4.5) and then integrating on [0, t], 0 < t < tlm, we obtain 1 2 \u2016u\u2032lm(t)\u20162H + 1 2 \u2016ulm(t)\u20162V + 1 \u03c1+ 1 (|ulm(t)|\u03c1, ulm(t))H + d0 \u222b t 0 \u2016u\u2032lm(s)\u20162L2(\u03931)ds \u2264 1 2 \u2016u1 l \u20162H + 1 2 \u2016u0\u20162V = 1, \u2200x \u2208 \u2126, \u03d50 \u2208 D(\u2126), \u03d5l \u2208 D(Ul), l = 1, 2, . . .", "mime": "application/pdf"}, {"id": "ejde-1060", "words": "9981", "extension": ".pdf", "flesch": "72", "author": "Caraballo, Tomas; Ezzine, Faten; Hammami, Mohamed Ali", "title": "Practical stability of stochastic differential delay equations driven by G-Brownian motion with general decay rate", "date": "2024", "keywords": "brownian; delay; differential; equations; lyapunov; motion; r(t; stability; stochastic; t t0", "summary": "Now, we consider the nonlinear stochastic differential delay equations driven by a G-Brownian motion in the form dx(t) = f(t, xt)dt+ h(t, xt)d\u27e8B\u27e9t + g(t, xt)dBt, t \u2265 t0, (3.1) where Bt is a one-dimensional G-Brownian motion, with Bt \u223c N (0, [\u03c32t, \u03c3\u03042t]), and (\u27e8B\u27e9)t\u22650 is the quadratic variation process of the G-Brownian, and f : Based on this fact, we deduce that V (t, xt) \u2264 V (0, x0) + \u03c61 ( K 2N )\u22121 ln K \u2212 1 2N + \u222b t t0 LV (s, xs)ds + \u03c3\u03042 \u222b t t0 \u03c61(s)\u2225Vs(s, xs)g(s, xs)\u22252ds, for t0 \u2264 t \u2264 K/2N and K \u2264 K0(\u03b5, \u03c9).", "mime": "application/pdf"}, {"id": "ejde-1061", "words": "10776", "extension": ".pdf", "flesch": "80", "author": "Lopera, Emer; Recova, Leandro; Rumbos, Adolfo", "title": "Multiplicity results for Schrodinger type fractional p-Laplacian boundary value problems", "date": "2024", "keywords": "problem; solution; theorem", "summary": "In this work, we study the existence and multiplicity of solutions to the problem \u2212(\u2206)spu+ V (x)|u|p\u22122u = \u03bbf(u), x \u2208 \u2126; u = 0, x \u2208 RN\\\u2126, where \u2126 \u2282 RN is an open bounded set with Lipschitz boundary \u2202\u2126, N \u2a7e 2, V \u2208 L\u221e(RN ), and (\u2212\u2206)sp denotes the fractional p-Laplacian with s \u2208 (0, 1), 1 < p, sp < N , \u03bb > 0, and f : R \u2192 R is a continuous function. = 1, for x \u2208 \u2126; u = 0, in RN\\\u2126, (7.1) has a positive weak solution.", "mime": "application/pdf"}, {"id": "ejde-108", "words": "5136", "extension": ".pdf", "flesch": "68", "author": "Almeida, Adilson; Chemetov, Nikolai V.; Cipriano, Fernanda", "title": "Uniqueness for optimal control problems of two-dimensional second grade fluids", "date": "2022", "keywords": "control; fluids; problem; solution", "summary": "In this article, we study second grade fluids, which belong to the class of non- Newtonian complex viscoelastic fluids of differential type. From the mathematical point of view, the equations governing the evolution of second grade fluids are strongly nonlinear partial differential equations.", "mime": "application/pdf"}, {"id": "ejde-1083", "words": "26531", "extension": ".pdf", "flesch": "76", "author": "Luczak, Brian B.", "title": "A priori estimates for the linearized relativistic Euler equations with a physical vacuum boundary and an ideal gas equation of state", "date": "2025", "keywords": "+ r; 2(\u03b3\u22121; 2\u2212\u03b3; 2\u2212\u03b3 \u03b3\u22121; boundary; derivatives; ejde-2025/10; equations; estimates; following; h2k; lemma; norm; order; r 2\u2212\u03b3; r r; remark; section; subcritical; t r\u0303; terms; use; \u03b3 \u2212", "summary": "\u2202iu i + ( (\u03b3 \u2212 1) (u0)2 u\u03030r \u2212 \u03b3 \u2212 1 u0 r\u0303 ) \u2202tr = \u2212 ui u0 \u2202ir \u2212 \u03b3 \u2212 1 u0 r\u2202iu i \u2212 \u03b3 \u2212 1 u0 r ( Ci 1\u2202iu 0 + Ci 2\u2202ir + C3r\u2202iu i ) implies \u2202tr\u0303 = \u2212 ui u0 \u2202ir\u0303 \u2212 \u03b3 \u2212 1 u0 r\u2202iu\u0303 i \u2212 \u03b3 \u2212 1 u0 r ( \u2202tu\u0303 0 ) + uiu\u03030 \u2212 u0u\u0303i (u0)2 \u2202ir + ( (\u03b3 \u2212 1) (u0)2 u\u03030r \u2212 \u03b3 \u2212 1 u0 r\u0303 )", "mime": "application/pdf"}, {"id": "ejde-1084", "words": "6234", "extension": ".pdf", "flesch": "82", "author": "Xin; Xinglong", "title": "Persistence properties of solutions for multi-component Novikov equations", "date": "2025", "keywords": "equation", "summary": "For p > 1, if the initial data satisfies for some C > 0, \u2225U0(x)I(x)\u2225Lp + \u2225U0,x(x)I(x)\u2225Lp \u2264 C, then the solution satisfies \u2225U(t, \u00b7)I\u2225Lp + \u2225Ux(t, \u00b7)I\u2225Lp \u2264 C, EJDE-2025/27 MULTI-COMPONENT NOVIKOV EQUATIONS 7 uniformly in the interval [0, T ], where for \u03b1 \u2208 [0,\u221e) and K \u2208 R+, the weighted function I(x) is given by I(x) = { (ln(e2 + |x|))\u03b1, |x| \u2208 [0, T ], Y (t) \u2264 CY (0) \u2264 C (\u2225U0(x)I(x)\u2225Lp + \u2225U0,x(x)I(x)\u2225Lp + \u2225U0,xxI\u2225Lp) .", "mime": "application/pdf"}, {"id": "ejde-1087", "words": "6675", "extension": ".pdf", "flesch": "77", "author": "Nunes, Ruikson; Nunez-Chavez, Miguel R.", "title": "Exact boundary controllability for wave equations with fixed and moving boundaries in two-dimensional convex-complemented domains", "date": "2025", "keywords": "boundary; decay; problem; wave", "summary": "Making \u03c4 = T \u2212 t in latest inequality and observing that u(\u00b7, t) = v(\u00b7, T \u2212 t) is solution of (2.6) satisfying the estimate (2.7). Wave equation; energy decay; exact boundary controllability; non-cylindrical domains; moving boundary domains.", "mime": "application/pdf"}, {"id": "ejde-109", "words": "12917", "extension": ".pdf", "flesch": "84", "author": "Burton, Theodore A.; Purnara, Ioannis K.", "title": "Open mappings: The case for a new direction in fixed point theory", "date": "2022", "keywords": "point; solution", "summary": "Moreover, writing the second summand in the right-hand-side of (9.10) as \u03b2 t2 + 1 sin ( t2 + x2(t) t2 + 1 )\u222b t 0 s (t2 + 1)te\u2212t + |x(s)|p 1 + s2 + t2 ds t \u2265 0, it is not difficult to see that for any bounded function x it holds 0 \u2264 \u03b2 t2 + 1 \u2223\u2223\u2223 sin( t2 + x2(t) t2 + 1 )\u2223\u2223\u2223 \u222b t 0 s (t2 + 1)te\u2212t + |x(s)|p 1 + s2 + t2 ds \u2264 \u03b2te\u2212t t2 + 1 \u222b t 0 sds+ \u03b2\u2016x\u2016p t2 + 1 \u222b t 0 s 1 + s2 + t2 ds \u2264 \u03b2t3e\u2212t 2(t2 + 1) + \u03b2\u2016x\u2016p t2 + 1 \u222b t 0 s 1 + t2 ds \u2264 \u03b2te\u2212t + \u03b2\u2016x\u2016pt2 2(t2 + 1)2 , and so lim t\u2192\u221e \u03b2 t2 + 1 sin ( t2 + x2(t) t2 + 1 )\u222b t 0 s (t2 + 1)te\u2212t + |x(s)|p 1 + s2 + t2 ds = 0. + \u222b t 0 K(t, s)v(t, s, x(s))ds, for their importance in applied mathematics and the fact that the integral term un- der a wide set of conditions will define a compact map", "mime": "application/pdf"}, {"id": "ejde-1093", "words": "12549", "extension": ".pdf", "flesch": "80", "author": "Gingolld, Harry; Quaintance, Jocelyn", "title": "Spherical compactifications of central force equations", "date": "2025", "keywords": "lim; m\u2192\u221e; radius", "summary": "= \u03b32 + (1\u2212 \u03b32)r2 = \u03b32 + (1\u2212 \u03b32)(q21 + q22 + \u00b7 \u00b7 \u00b7+ q2n). \u2212 2 [ \u03b32 \u2212 \u03b32 (\u03b32 + \u221a \u03c9 r2 + \u03b32 ) \u2212 \u03b32 (\u03b32 + \u221a \u03c9\u0302 r\u03022 + \u03b32 )] , (3.27) where r2 := QTQ, r\u03022 := Q\u0302T Q\u0302, \u03c9 := \u03b32 + (1\u2212 \u03b32)r2, \u03c9\u0302 := \u03b32 + (1\u2212 \u03b32)r\u03022; see Figure 4.", "mime": "application/pdf"}, {"id": "ejde-1096", "words": "9515", "extension": ".pdf", "flesch": "81", "author": "Yang, Minbo; Zhou, Fan", "title": "Existence and multiplicity of solutions to quasilinear Dirac-Poisson systems", "date": "2025", "keywords": "dirac; energy; lemma; solutions; system", "summary": "(2.1) We will write A0 := i\u03b1 \u00b7 \u2207 \u2212 a\u03b2, A\u03c9 := A0 \u2212 \u03c9 denote the self-adjoint operator on L2 := L2(R3,C4) with domain D(A\u03c9) \u2282 H1 := H1(R3,C4). = 1 2 (\u2225u+\u22252 \u2212 \u2225u\u2212\u22252)\u2212 \u0393\u03b5(u)\u2212 \u222b R3 F (x, |u|) dx \u2264 \u2225u+\u22252 \u2212 1 2 \u2225u\u22252 \u2212 \u222b R3 K1(x)G(|u|) dx \u2264 1 c2N |u+|2q \u2212 c0K1,inf |u+|qq \u2212 1 2 \u2225u\u22252 \u2264 q", "mime": "application/pdf"}, {"id": "ejde-110", "words": "6770", "extension": ".pdf", "flesch": "82", "author": "Afrouzi, Ghasem A.; Chung, Nguyen Thanh; Naghizadeh, Zohreh", "title": "Multiple solutions for p(x)-Kirchhoff type problems with Robin boundary conditions", "date": "2022", "keywords": "d\u03c3x; p(x; \u03b2(x", "summary": "Hence, F (x, \u03c4t) \u2265 \u03c4\u00b5F (x, t), \u2200x \u2208 \u2126, t \u2208 R, \u03c4 \u2265 1. (2.3) Let \u03d5 \u2208 C\u221e0 (\u2126) and \u03d5 6\u2261 0 such that \u222b \u2126 F (x, \u03d5) dx > 0, by (A1) we have J\u03bb(\u03c4\u03d5) Introduction In this article, we study the existence of weak solutions for p(x)-Kirchhoff type problems with Robin boundary conditions \u2212M (\u222b \u2126 1 p(x) |\u2207u|p(x) dx+ \u222b \u2202\u2126 \u03b2(x) p(x) |u|p(x) d\u03c3x ) div ( |\u2207u|p(x)\u22122\u2207u ) = f(x, u) + \u03bbg(x), x \u2208 \u2126, |\u2207u|p(x)\u22122 \u2202u \u2202\u03bd + \u03b2(x)|u|p(x)\u22122u = 0, x \u2208 \u2202\u2126, (1.1) where \u2126 is a bounded domain in RN with smooth boundary \u2202\u2126, \u2202u \u2202\u03bd is the outer normal derivative, d\u03c3x is the measure on the boundary \u2202\u2126, \u03b2 \u2208 L\u221e(\u2202\u2126), \u03b2\u2212 := infx\u2208\u2202\u2126 \u03b2(x) > 0, p \u2208 C+(\u2126), 1 < p\u2212 := infx\u2208\u2126 p(x) \u2264 p+ := maxx\u2208\u2126 p(x) <", "mime": "application/pdf"}, {"id": "ejde-1105", "words": "7752", "extension": ".pdf", "flesch": "81", "author": "Xu, Tianyuan; Liu, Gege; Yin, Jingxue", "title": "Existence and stability of forced waves for p-Laplace equations in a shifting habitat", "date": "2025", "keywords": "waves; \u03d5(\u03be", "summary": "\u222b\u222b Q\u03c4 ( \u03b2 2 + u1 + u2 \u2212 r(\u03be))u2\u03b1n(x)e \u2212\u03b2tdxdt +D \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x)(u1x \u2212 u2x)e \u2212\u03b2t\u03b1n(x)dxdt = \u2212D \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x)(u1 \u2212 u2)e \u2212\u03b2t\u03b1\u2032 n(x)dxdt \u2264 D \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x) 2|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt+ \u222b\u222b Q\u03c4 u2|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt. (3.22) Noticing that \u03b1\u2032 n(x) = 0 for |x| < n and |x| > n+ 1, we see that D \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x) 2|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt+ \u222b\u222b Q\u03c4 u2|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt \u2264 2D \u222b\u222b Q\u03c4 (|u1x|2(p\u22121) + |u2x|2(p\u22121))|\u03b1\u2032 n(x)|dxdt+ \u222b\u222b Q\u03c4 u2|\u03b1\u2032 n(x)|dxdt \u2264 C, where C is independent of n. Letting n \u2192 \u221e in (3.22), we obtain\u222b\u222b Q\u03c4 u2e\u2212\u03b2tdxdt+D \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x)(u1x \u2212 u2x)e \u2212\u03b2tdxdt \u2264 C. (3.23) Recalling (3.22) and noticing that uix(i = 1, 2) are bounded, we infer that D \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x) 2|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt+D \u222b\u222b Q\u03c4 u2|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt \u2264 D(p\u2212 1)(\u2225u1x\u2225L\u221e + \u2225u2x\u2225L\u221e)p\u22122 \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x)(u1x \u2212 u2x)|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt +D \u222b\u222b Q\u03c4 u2|\u03b1\u2032 n(x)|e\u2212\u03b2tdtdx \u2264 C \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x)(u1x \u2212 u2x)|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt+D \u222b\u222b Q\u03c4 u2|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt. From (3.23), the above inequality reduces to C \u222b\u222b Q\u03c4 (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x)(u1x \u2212 u2x)|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt+D \u222b\u222b Q\u03c4 u2|\u03b1\u2032 n(x)|e\u2212\u03b2tdxdt \u2192 0, as n \u2192 \u221e. Now, (3.22) shows that 1 2 \u222b R e\u2212\u03b2tu2(x, \u03c4)dx+ \u222b\u222b Q\u03c4 e\u2212\u03b2t(u2 + (|u1x|p\u22122u1x \u2212 |u2x|p\u22122u2x)(u1x \u2212 u2x))dxdt \u2264 0, which implies that u1 = u2 in Q\u03c4 .", "mime": "application/pdf"}, {"id": "ejde-1109", "words": "7287", "extension": ".pdf", "flesch": "82", "author": "Zeng, Lingzhong; Zhou, Ziyi", "title": "Eigenvalue bounds for the clamped plate problem of L^2_xi operator", "date": "2025", "keywords": "e\u27e8\u03be; i=1; j=1; x\u27e9g0dv; \u03b3k+1", "summary": "G = k\u2211 i,j=1 (\u0393k+1 \u2212 \u0393j) aijtij + k\u2211 i,j=1 (\u0393j \u2212 \u0393i) aijtij = k\u2211 j,i=1 (\u0393k+1 \u2212 \u0393i) aijtji + k\u2211 i,j=1 sijtij = \u2212 k\u2211 j,i=1 (\u0393k+1 \u2212 \u0393i) aijtij + k\u2211 i,j=1 sijtij = \u2212G+ k\u2211 [ \u0393i (\u0393k+1 \u2212 \u0393i) ]1/2 , (1.8) which is sharper than \u0393k+1 \u2264 [ 1 + 8(n+ 2) n2 ]1 k k\u2211 i=1 \u0393i. (1.9) EJDE-2025/31 EIGENVALUE BOUNDS FOR THE CLAMPED PLATE PROBLEM 3 We note that, in fact, inequality (1.9) is better than inequality (1.5) given by Payne, Po\u0301lya and Weinberger.", "mime": "application/pdf"}, {"id": "ejde-111", "words": "13537", "extension": ".pdf", "flesch": "77", "author": "Barkatou, Moulay; Carnicero, F\u00e9lix \u00c1lvaro; Sanz, Fernando", "title": "Turrittin's normal forms for linear systems of meromorphic ODEs over the real field", "date": "2023", "keywords": "block; case; diagonal; gauge; matrix; polynomial; proof; system; theorem; transformation", "summary": "We present versions of real (formal and polynomial) normal forms for any system, in such a way EJDE-2023/79 TURRITTIN\u2019S THEOREM 3 that they can be obtained by transformations written in the base field K, without passing through the algebraic closure K = K( \u221a \u22121). Now, Turrittin\u2019s results for the case where K = K can be stated in the two following theorems.", "mime": "application/pdf"}, {"id": "ejde-1110", "words": "12225", "extension": ".pdf", "flesch": "81", "author": "Son, Dang Thanh", "title": "Long-time behavior of solutions to the 2D magnetic B\\'enard problem in porous media on unbounded domains", "date": "2025", "keywords": "attractor; equations; existence; lemma; l\u0303r+1; problem; r\u22121; solution", "summary": "In the next Lemma, we show that the map \u039b(t; z0) is bounded and the semigroup {S(t)}t\u22650 is uniformly differentiable on global attractor A, i.e., lim \u03b5\u21920 sup 0<|z\u03040\u2212z0|<\u03b5, z\u03040,z0\u2208A |S(t)z\u03040 \u2212 S(t)z0 \u2212 \u039b(t; z0)(z\u03040 \u2212 z0)| |z\u03040 \u2212 z0| = 0. (5.2) Then for r = 1, 3, there exists a constantM(|z\u03040|, |z0|) such that |S(t)z\u03040 \u2212 S(t)z0 \u2212 \u039b(t; z0)(z\u03040 \u2212 z0)| \u2264M |z\u03040 \u2212 z0|, (5.3) where the linear operator \u039b(t; z0) for t > 0 is the solution operator of the prob- lem (5.1).", "mime": "application/pdf"}, {"id": "ejde-1115", "words": "22418", "extension": ".pdf", "flesch": "77", "author": "Achleitner, Franz ; Cuesta, Carlota M.; Diez-Izagirre, Xuban", "title": "Existence of undercompressive travelling waves of a non-local generalised Korteweg-de Vries-Burgers equation", "date": "2025", "keywords": "2\u2212\u03b1; lemma; non; proof; solutions; theorem; \u03b7 0; \u03b7inflex", "summary": "Then, there exists an order one constant C > 0, such that \u03d5\u03c4 \u2208 \u03d5\u2212 +H2(I\u03c4,\u03b5), \u2225\u03d5\u03c4 \u2212 \u03d5\u2212 \u2212 e\u03bb\u03c4\u03be\u2225H2(I\u03b5) \u2264 C\u03b52 . \u2212 \u03be) near \u03be\u2217, or in terms of the variable \u03b7 |\u03a6\u03c4 (\u03b7) + \u03d5c| > C \u221a \u03c4 (\u03b7\u2217 \u2212 \u03b7) .", "mime": "application/pdf"}, {"id": "ejde-1119", "words": "6314", "extension": ".pdf", "flesch": "82", "author": "Nie, Yuanyuan; Leng, Yan; Zhao, Xu; Zhou, Qian", "title": "Critical Fujita exponents for a class of quasilinear coupled parabolic \u00a0equations", "date": "2025", "keywords": "t)\u03c8l(x)dx; u(x; |x|+", "summary": "Introduction In this article, we study the critical Fujita exponent for the Cauchy problem of quasilinear coupled parabolic equations \u2202u \u2202t = \u2206um + (|x|+ 1)\u03bbvp, x \u2208 Rn, t > 0, (1.1) \u2202v \u2202t = \u2206vm + (|x|+ 1)\u00b5uq, x \u2208 Rn, t > 0, (1.2) u(x, 0) = u0(x), v(x, 0) = v0(x), x \u2208 Rn, (1.3) where p, q > m > 1, \u03bb \u2265 0, \u00b5 = \u03bb(q \u2212m) + 2(q \u2212 p) p\u2212m \u2265 0 (1.4) and 0 \u2264 u0, v0 \u2208 C0(Rn) are nontrivial. It was demonstrated that the Cauchy problem of the heat equation \u2202u \u2202t = \u2206u+ up, x \u2208 Rn, t > 0 admits no nontrivial nonnegative global solution when 1 < p < pc = 1 + 2/n, otherwise, it admits both nontrivial global (with small initial data) and nonglobal nonnegative (with large initial data) solutions when p > pc.", "mime": "application/pdf"}, {"id": "ejde-112", "words": "11624", "extension": ".pdf", "flesch": "86", "author": "Goyal, Sarika; Sharma, Tarun", "title": "Fractional Kirchhoff Hardy problems with weighted Choquard and singular nonlinearity", "date": "2022", "keywords": "dx dy; q \u2212; y|\u00b5|y|\u03b1; y|\u00b5|y|\u03b1 dx; |x|\u03b1|x\u2212; \u2212 \u222b; \u222b \u03c9", "summary": "p ((uk(y)\u2212 u0(y))) p |x|\u03b1|x\u2212 y|\u00b5|y|\u03b1 dx dy = 0. (4.27) Using (4.27) in (4.26), we have 0 \u2265 ( c+ dv2\u03b8\u22122 ) lim k\u2192\u221e \u2016uk \u2212 u0\u20162 \u2212 \u03b3 lim k\u2192\u221e \u2016uk \u2212 u0\u20162H = c [ lim k\u2192\u221e \u2016uk \u2212 u0\u20162 \u2212 \u03b3 c lim k\u2192\u221e \u2016uk \u2212 u0\u20162H ] + dv2\u03b8\u22122 lim k\u2192\u221e \u2016uk \u2212 u0\u20162. = (1 2 \u2212 1 2p ) hc,\u03b3t 2 1\u2212q \u2212 \u03bb ( 1 1\u2212 q \u2212 1 2p ) \u2016l\u2016mS \u2212(1\u2212q) 2 t, which has minimum at tmin := (\u03bb(2p+ q \u2212 1)S \u2212(1\u2212q) 2 \u2016l\u2016m (2p\u2212 2)hc,\u03b3 ) 1\u2212q 1+q .", "mime": "application/pdf"}, {"id": "ejde-113", "words": "6956", "extension": ".pdf", "flesch": "66", "author": "Fresneda Portillo, Carlos; Woldemicheal, Zenebe W.", "title": "Boundary-domain integral equations for Dirichlet diffusion problems with non-smooth coefficient", "date": "2022", "keywords": "boundary; domain; equations; hs\u2212; operator; parametrix; solution; theorem", "summary": "Let \u03c1 \u2208 D(\u2126), the volume poten- tial and the remainder potential operator, corresponding to parametrix (3.1) and remainder (3.2) are defined as P\u03c1(y) := \u222b R3 P (x, y)\u03c1(x) dx, y \u2208 R3, P\u03c1(y) := \u222b \u2126 P (x, y)\u03c1(x) dx, y \u2208 \u2126, R\u03c1(y) Domain and boundary integral operators After replacing the parametrix in the Green identities, we obtain an integral representation formula of the solution in terms of potential-type operators whose kernel is somehow related to the parametrix.", "mime": "application/pdf"}, {"id": "ejde-1137", "words": "8020", "extension": ".pdf", "flesch": "77", "author": "Liu, Ling", "title": "Global well-posedness to a multidimensional parabolic-elliptic-elliptic attraction-repulsion chemotaxis system", "date": "2025", "keywords": "chemotaxis; system; tmax", "summary": "6 L. LIU EJDE-2025/26 Then, recalling \u03be\u03b3 = \u03c7\u03b1, (1.1), (1.6), (1.7) can be rewritten as ut = \u2206u\u2212\u2207 \u00b7 (u\u2207s), x \u2208 \u2126, t \u2208 (0, Tmax), 0 In the absence of chemorepulsive chemical (i.e. chemorepellent), namely \u03be = 0, w is decoupled from the system (1.1) and the first two equations of (1.1) comprises a classical Keller-Segel model ut = \u2206u\u2212 \u03c7\u2207 \u00b7 (u\u2207v), x \u2208 \u2126, t > 0, 0 = \u2206v", "mime": "application/pdf"}, {"id": "ejde-1144", "words": "6851", "extension": ".pdf", "flesch": "82", "author": "Xing, Zhaojun", "title": "Single-component regularity criterion and inviscid limit for axially symmetric MHD-Boussinesq systems", "date": "2025", "keywords": "boussinesq; mhd; system; \u22252l2", "summary": "\u2225pLp + \u222b t 0 \u222b R3 |\u2207H(s, x)|2|H(s, x)|p\u22122 dx ds \u2264 \u2225H0\u2225pLp , \u2225H(t, \u00b7)\u2225L\u221e \u2264 \u2225H0\u2225L\u221e , \u2225\u03c1(t, \u00b7)\u2225pLp + \u222b t 0 \u222b R3 |\u2207\u03c1(s, x)|2|\u03c1(s, x)|p\u22122 dx ds \u2264 \u2225\u03c10\u2225pLp , \u2225\u03c1(t, \u00b7)\u2225L\u221e \u2264 \u2225\u03c10\u2225L\u221e . (3.1) (ii) for (u0, h0, \u03c10) \u2208 L2 and t \u2208 R+, \u2225(u, h)(t, \u00b7)\u22252L2 + \u222b t 0 \u2225\u2207h (s, \u00b7) \u22252L2 ds \u2264 C0(1 + t)2, (3.2) where C0 depends only on \u2225(u0, h0, \u03c10)\u2225L2 . Proof. This ends up with \u2225\u2207H(t, \u00b7)\u22252L2 + \u222b t 0 \u2225\u22072H(s, \u00b7)\u22252L2 ds \u2272 \u2225\u2207H0\u22252L2 + \u222b t 0 \u2225\u2126(s, \u00b7)\u22252L2\u2229L6\u2225\u2207h(s, \u00b7)\u22252L2 ds. (3.6) Then, we obtain the estimate of N .", "mime": "application/pdf"}, {"id": "ejde-116", "words": "8846", "extension": ".pdf", "flesch": "72", "author": "Zhao, Zhihong; Shaochun, Shaochun; Lu, Yulan", "title": "Mathematical models for the transmission of malaria with seasonality and ivermectin", "date": "2022", "keywords": "ivermectin; malaria; model; rate; transmission", "summary": "In this section, we propose a seasonal effect of delay malaria transmission model taking into account the treatment and ivermectin. Recently, [18] mod- elled the effect of ivermectin on malaria transmission control by ordinary differential equations and the results showed that ivermectin was significantly more effective in malaria control compared to the no-intervention state.", "mime": "application/pdf"}, {"id": "ejde-1179", "words": "4145", "extension": ".pdf", "flesch": "74", "author": "Ramos, Gustavo de Paula", "title": "Asymptotic profile of least energy solutions to the nonlinear Schrodinger-Bopp-Podolsky system", "date": "2025", "keywords": "2p\u2212; energy; schro\u0308dinger; solutions", "summary": "For instance, [3, 2, 10, 11, 15, 21, 25] addressed the existence of least energy solutions; [7, 12, 13] considered the mass-constrained problem; [8, 9, 17, 23, 22] obtained sign-changing solutions; and [4, 6] considered semiclassical states. For instance, [5, Theorem 1.3] proved such a result for radial solutions; [7, Theorem D] extended this conclusion for least energy solutions to the mass-constrained system for 2 < p < 14/5 and a sufficiently small mass \u03c1 (notice that these solutions are also radial due to [7, Theorem C]); [20, Theorem 1.3] showed that solutions to the associated eigenvalue problem in a bounded smooth domain also have such an asymptotic profile and, more recently, [4, Theorem 1.7] verified such a behavior for the critical nonlinear SBP system in the semiclassical regime under the effect of an external effective potential V : R3 \u2192 [0,\u221e[ which vanishes at a point x0 \u2208 R3.", "mime": "application/pdf"}, {"id": "ejde-118", "words": "7475", "extension": ".pdf", "flesch": "82", "author": "Barraza Martinez, Bienvenido; Hernandez Monzon, Jairo; Vergara Rolong, Gustavo", "title": "Exponential stability of a damped beam-string-beam transmission problem", "date": "2022", "keywords": "beam; problem; stability; transmission", "summary": "\u2212 \u3008i(l2 \u2212 x)g\u20321,n, \u03bbnv1,n\u3009L2(I2) \u2212 i(l2 \u2212 l1)\u03bbng1,n(l1)v1,n(l1) + \u3008v\u2032\u20321,n, (l2 \u2212 x)v\u20321,n\u3009L2(I2). \u2212 \u3008i(l2 \u2212 x)g\u20321,n, \u03bbnv1,n\u3009L2(I2) \u2212 i(l2 \u2212 l1)g1,n(l1)\u03bbnv1(l1)\u2212 \u3008\u03b2v2,n, (l2 \u2212 x)v\u20321,n\u3009L2(I2) + \u3008ig1,n, \u03bbnv1,n\u3009L2(I2) } + \u2016\u03bbnv1,n\u20162L2(I2) + \u2016v\u20321,n\u20162L2(I2).", "mime": "application/pdf"}, {"id": "ejde-1183", "words": "15629", "extension": ".pdf", "flesch": "78", "author": "Girg, Petr; Kotrla, Lukas", "title": "Modeling of groundwater flow in porous medium layered over inclined impermeable beds", "date": "2025", "keywords": "cos\u03c6+; flow; function; medium; problem; proof; sin\u03c6; sin\u03c6|p\u22122; solution; u(x; u\u2032(1; water; \u2225f\u2225l1(\u22121,1", "summary": "Porous medium; filtration; nonlinear Darcy\u2019s law; p-Laplacian; pressure-to-velocity power law. Mathematical model of water flow in porous medium layered over an inclined impermeable bed 2.1.", "mime": "application/pdf"}, {"id": "ejde-1189", "words": "8024", "extension": ".pdf", "flesch": "82", "author": "Yang, Zhi-Jiao; Zhang, Guo-Bao; He, Juan", "title": "Traveling wavefronts for a discrete diffusive Lotka-Volterra competition system with nonlocal nonlinearities", "date": "2025", "keywords": "i\u2208z; system", "summary": "[32] further studied the stability of traveling wave solutions of system (1.3) with relatively large speed by the weighted energy method combining with the comparison principle. It is well known that traveling wave solutions can describe the transitions between different states of a physical system, propagation of patterns, and domain invasion of species in population biology (see, e.g., [6]).", "mime": "application/pdf"}, {"id": "ejde-119", "words": "6301", "extension": ".pdf", "flesch": "82", "author": "Zhang, Xuping", "title": "Lower and upper solutions for delay evolution equations with nonlocal and impulsive conditions", "date": "2002", "keywords": "conditions; equations; v(0; w(0", "summary": "We mention that in 2012, Chuong and Ke [10] studied the delay evolution inclu- sions involving nonlocal and impulsive conditions u\u2032(t) +Au(t) \u2208 F (t, u(t), ut), t \u2208 Evidently, PC([\u2212h, a], X) and B are also order Banach spaces with partial order \u201c \u2264 \u201d reduced by the positive function cones KPC = {u \u2208 PC([\u2212h, a], X) : u(t) \u2265 \u03b8, t \u2208", "mime": "application/pdf"}, {"id": "ejde-1193", "words": "9619", "extension": ".pdf", "flesch": "88", "author": "He, Juhua; Wu, Ke; Zhou, Fen", "title": "Existence of nontrivial solutions for biharmonic equations with critical growth", "date": "2025", "keywords": "2\u2217\u2217", "summary": "Again by (2.6)-(2.11), there exists a small \u03b51 \u2208 (0, \u03b52) such that I(tw\u03b5) \u2265 t2 2 \u222b R5 (\u2206w\u03b5) 2dx\u2212 t2 \u2217\u2217 2\u2217\u2217 \u222b R5 |w\u03b5|2 \u2217\u2217 dx\u2212 \u03b1 tp p \u222b R5 |w\u03b5|pdx \u2265 t2 4 S 5/4 \u2217\u2217 \u2212 t2 \u2217\u2217 2\u2217\u2217 S 5/4 \u2217\u2217 \u2212 \u03b1C\u03b55\u2212 p 2 tp 6 J. HE, K. WU, F. ZHOU EJDE-2025/69 for all \u03b5 \u2208 (0, \u03b51). Hence, I(t\u03b5w\u03b5) \u2265 max 0\u2264t\u22641 { t 2 4 S 5/4 \u2217\u2217 \u2212 t2 \u2217\u2217 2\u2217\u2217 S 5/4 \u2217\u2217 \u2212 \u03b1C\u03b55\u2212 p 2 tp} \u2265 \u03b7 2 .", "mime": "application/pdf"}, {"id": "ejde-1196", "words": "10281", "extension": ".pdf", "flesch": "76", "author": "Agudelo, Oscar; Holubova, Gabriela; Kudlac, Martin", "title": "Variational and numerical aspects of a system of ODEs with concave-convex nonlinearities", "date": "2025", "keywords": "du0; dv0; proof; solutions", "summary": "We show multiplicity of nonnegative solutions for a range of the parameter \u03bb and discuss the regularity and symmetry of nonnegative solutions. In [4], the authors study existence, nonexistence and multiplicity of nonnegative solutions of the single equation \u2212v\u2032\u2032", "mime": "application/pdf"}, {"id": "ejde-12", "words": "4354", "extension": ".pdf", "flesch": "74", "author": "Vidhyaa, Kumar S.; Thandapani, Ethiraju; Alzabut, Jehad; Ozbekler, Abdullah", "title": "Oscillation criteria for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term", "date": "2023", "keywords": "equations; oscillation", "summary": "[21] B. Kamaraj, R. Vasuki; Oscillation of second order difference equations with a superlinear neutral term, J. Adv. 12 K. S. VIDHYAA, E. THANDAPANI, J. ALZABUT, A. O\u0308ZBEKLER EJDE-2023/45 [26] S. Meharbanu, S. Nalini; Oscillation of second order difference equations with several super- linear neutral terms, Adv. Differ.", "mime": "application/pdf"}, {"id": "ejde-120", "words": "9824", "extension": ".pdf", "flesch": "70", "author": "Li, Shangzhi; Guo, Shangjiang", "title": "Dynamics of stochastic Lotka-Volterra predator-prey models driven by three independent Brownian motions", "date": "2022", "keywords": "predator; prey; solution; system", "summary": "For the parameters \u00b51 = \u00b52 = \u03c11 = \u03c12 = 0.1, we have \u03bb2 \u2248 0.4485 and \u03bb1 \u2248 0.8868. Similarly to [23, Proposition 3.2], we conclude that there are T = T (\u03c2) and \u03b41 = \u03b41(\u03c2) > 0 such that (4.5) holds, which implies that X2,x is away from zero for all x \u2208 R2,\u25e6 + .", "mime": "application/pdf"}, {"id": "ejde-1208", "words": "5891", "extension": ".pdf", "flesch": "84", "author": "Jing, Zhao; Liu, Zhenhai; Papageorgiou, Nikolaos S.", "title": "Weighted (p,q)-equations with gradient dependent reaction", "date": "2025", "keywords": "1,p", "summary": "Introduction Let \u2126 \u2286 RN be a bounded domain with a C2-boundary \u2202\u2126. In this article we study the parametric Dirichlet problem \u2212\u2206a1 p u(z)\u2212\u2206a2 q u(z) = f(z, u(z)) + \u03bb|Du(z)|p\u22121 in \u2126, u|\u2202\u2126 = 0, 1 <", "mime": "application/pdf"}, {"id": "ejde-1217", "words": "11379", "extension": ".pdf", "flesch": "86", "author": "Borsuk, Mikhail", "title": "Neumann-Robin problem for p(x)-Laplacian equations in a domain with the boundary edge", "date": "2025", "keywords": "j\u22121; p+ \u2212; \u2212 k)+; \u222a\u03c9r0", "summary": "(p\u2212 \u2212 1)\u2212 2 s( j\u27e8(p\u2212 \u2212 1)\u03ba + 3\u2212 p\u2212\u27e9 \u2212 1 )( j\u27e8(p+ \u2212 1)\u03ba \u2212 2 s + 2\u27e9 \u2212 1 ) . p\u2212\u27e9 \u2212 1 )( j\u27e8(p+ \u2212 1)\u03ba \u2212 2 s + 2\u27e9 \u2212 1 )} j j\u22121 .", "mime": "application/pdf"}, {"id": "ejde-122", "words": "6929", "extension": ".pdf", "flesch": "83", "author": "Fan, Xiaoting; Wang, Wei", "title": "Initial layer associated with Boussinesq systems for thermosolutal convection", "date": "2022", "keywords": "t \u03bb", "summary": "\u2202tT \u03bb In + (u\u03bbIn \u00b7 \u2207)T\u03bbIn = \u2206T\u03bbIn +R\u03bbIn,T , (3.18) \u2202tS \u03bb In + (u\u03bbIn \u00b7 \u2207)S\u03bbIn = \u03c4\u2206S\u03bbIn +R\u03bbIn,S , (3.19) u\u03bbIn|z=0,1 = 0, (3.20) (T\u03bbIn, S \u03bb In)|z=0 = (1, 1), (T\u03bbIn, S \u03bb In)|z=1 = (0, 0), (3.21) where the remainders R\u03bbIn,u, R\u03bbIn,T and R\u03bbIn,S are R\u03bbIn,u = \u2212 \u221e\u2211 i=2 \u03bbi(\u03bb[\u2202tu In,i + i\u2211 j=0 uIn,j \u00b7 \u2207uIn,i\u2212j ] +\u2207pIn,i \u2212\u2206uIn,i \u2212 \u221a Tak \u00d7 uIn,i \u2212 (RTT In,i \u2212RSSIn,i)k) + \u03bb3uIn,1 \u00b7 \u2207uIn,1, R\u03bbIn,T = \u2212 \u221e\u2211 i=2 \u03bbi ( \u2202tT In,i + i\u2211 j=0 uIn,j \u00b7 \u2207T EJDE-2022/33 INITIAL LAYER ASSOCIATED WITH BOUSSINESQ SYSTEMS 13 According to (3.69), (3.72), and (4.7), I3 = \u2212 \u222b D u\u03bba \u00b7 \u2207 ( (T\u03bbe )2 2 ) dx dy dz = \u2212 \u222b D \u2207 \u00b7 ( u\u03bba (T\u03bbe )2 2 )", "mime": "application/pdf"}, {"id": "ejde-1221", "words": "5461", "extension": ".pdf", "flesch": "84", "author": "Aparcana, Aldryn; Carhuas-Torre, Brandon; Castillo, Ricardo; Loayza, Miguel", "title": "Existence and non-existence of solutions for Hardy parabolic equations with singular initial data", "date": "2025", "keywords": "non", "summary": "At\u2212\u03b1 + \u222b t 0 (t\u2212 \u03c3)\u2212\u03b6f(\u03c3)\u03c6(\u03c3)d\u03c3 for t \u2208 (0, T ). Let t \u2208 (0, s) with s \u2208 (0, T ) and 1/q = 1\u2212 \u03f5 > 0.", "mime": "application/pdf"}, {"id": "ejde-123", "words": "6574", "extension": ".pdf", "flesch": "89", "author": "Wang, Sainan; Su, Yu", "title": "Existence of solution to critical Kirchhoff-type equation with dipole-type potential", "date": "2022", "keywords": "d1,2; equation; lim; rad(rn", "summary": "Specifically, the Schro\u0308dinger equation for the wave function of an electron interacting with a polar molecule can be written as H = \u2212 ~ 2m \u2206 + e x \u00b7D |x|3 \u2212 E, where D is the dipole moment of the molecule, e and m denote the charge and the mass of the electron, see [19]. We know that lim n\u2192\u221e \u2016vn\u20162\u03a6 = \u2016v\u20162\u03a6. By Bre\u0301zis-Lieb lemma again, we have lim n\u2192\u221e \u2016vn\u20162\u03a6 \u2212 lim n\u2192\u221e \u2016vn \u2212 v\u20162\u03a6 = \u2016v\u20162\u03a6, which implies lim n\u2192\u221e \u2016vn \u2212 v\u20162\u03a6 = 0.", "mime": "application/pdf"}, {"id": "ejde-1235", "words": "13422", "extension": ".pdf", "flesch": "83", "author": "Webb, Jeffrey R. L.", "title": "Inequalities for fractional derivatives via the Marchaud derivative", "date": "2025", "keywords": "continuous; derivative; fractional; u(t; \u03b3(1\u2212", "summary": "For \u03b5 > 0, the truncated fractional derivative is defined for t \u2208 (0, T ] by D\u03b1 M,\u03b5f(t) = f(t) \u0393(1\u2212 \u03b1)t\u03b1 + \u03b1 \u0393(1\u2212 \u03b1) \u03c8\u03b5(t), (2.11) where \u03c8\u03b5(t) : Then D\u03b1 Mu(t) exists for t \u2208 (0, T ].", "mime": "application/pdf"}, {"id": "ejde-124", "words": "5001", "extension": ".pdf", "flesch": "81", "author": "Sun, Rui; Liu, Duchao", "title": "Positive solution to quasilinear Schrodinger equations via Orlicz space framework", "date": "2022", "keywords": "equations; quasilinear; schro\u0308dinger; solutions", "summary": "[5] S. X. Chen; Existence of positive solutions for a class of quasilinear Schro\u0308dinger equations on RN , J. Math. [18] G. F. Li, Y. S. Huang, Z. Liu; Positive solutions for quasilinear Schro\u0308dinger equations with superlinear term, Complex Var.", "mime": "application/pdf"}, {"id": "ejde-1240", "words": "9114", "extension": ".pdf", "flesch": "83", "author": "Qin, Jiali; Hao, Jianghao", "title": "Asymptotic stability for thermodiffusion Timoshenko systems of type III", "date": "2025", "keywords": "stability; system; timoshenko", "summary": "Taking the derivative of L(t) with respect to t, using (3.2), (3.5), (3.7), (3.10), (3.14), (3.16) and (3.20), we have L\u2032(t) \u2264 \u2212 [ \u03c32N \u2212 cN1 \u2212 c ( 1 + 1 \u03b54 + 1 \u03b55 ) N4 \u2212 c ( 1 + 1 \u03b56 ) N5 \u2212 c ] \u222b 1 0 \u03b82xtdx \u2212 [ \u03b32N \u2212 cN1 \u2212 c ( 1 + 1 \u03b54 + 1 \u03b55 )", "mime": "application/pdf"}, {"id": "ejde-1242", "words": "8094", "extension": ".pdf", "flesch": "81", "author": "Feng, Meiqiang; Lu, Yichen", "title": "Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations", "date": "2025", "keywords": "f(x; h2(\u03c9; solutions; \u2229h1", "summary": "Uniqueness of nontrivial solutions In this section, we use the following assumptions on f : (A1) f(x, u) Carathe\u0301odory conditions for x \u2208 \u2126 and \u2212\u221e < u < +\u221e), and for fixed x \u2208 \u2126, f(x, u) is a decreasing function, that is f(x, u1) In this section, we suppose that f satisfies the following assumptions: (A3) f(x, u) satisfies Carathe\u0301odory conditions for x \u2208 \u2126 and \u2212\u221e < u < +\u221e), and there exists 0 < \u03c3 \u2264 N+4 N\u22124 such that |f(x, u)| \u2264 a+ b|u|\u03c3, a > 0, b > 0; (4.4) (A4) There exist 0 \u2264 \u03be < 1 2 and L > 0 such that F (x, u) = \u222b u 0 f(x, v)dv \u2264 \u03beuf(x, u), \u2200|u| \u2265 L, x \u2208 \u2126; (4.5) (A5)", "mime": "application/pdf"}, {"id": "ejde-1245", "words": "8383", "extension": ".pdf", "flesch": "79", "author": "Santos, Mauro L.; Freitas, Mirelson M.; Caljaro, Ronal Q.", "title": "Long-time dynamics and upper-semicontinuity of attractors for a porous-elastic system with nonlinear localized damping", "date": "2025", "keywords": "attractors; system; \u2212 \u222b", "summary": "[ \u03c1 \u222b L 0 utuxh\u03bb dx ]T 0 \u2212 [ J \u222b L 0 \u03d5t\u03d5xh\u03bb dx ]T 0 + \u03be \u222b T 0 \u222b L 0 \u03d52h\u2032\u03bb dx dt+ b \u222b T 0 \u222b L 0 ux\u03d5h \u2032 \u03bb dx dt + \u222b T 0 \u222b", "mime": "application/pdf"}, {"id": "ejde-125", "words": "7313", "extension": ".pdf", "flesch": "85", "author": "Razani, Abdolrahman; Figueiredo, Giovany M.", "title": "Weak solution by the sub-supersolution method for a nonlocal system involving Lebesgue generalized spaces", "date": "2022", "keywords": "a(x", "summary": "= f2(x, u, v)|\u2207u|\u03b12(x) Lq2(x) + g2(x, u, v)|\u2207u|\u03b32(x) Ls2(x) , with Dirichlet boundary condition, where \u2126 is a bounded domain in RN (N > 1) with C2 boundary. g1(x, u, v)|v|\u03b31(x) Ls1(x) in \u2126, \u2212A(x, |u|Lr2(x)) div ( a(|\u2207v|p2(x))|\u2207v|p2(x)\u22122\u2207v )", "mime": "application/pdf"}, {"id": "ejde-1250", "words": "10466", "extension": ".pdf", "flesch": "81", "author": "Xu, Ling", "title": "Asymptotic behavior of Kirchhoff type plate equations with nonlocal weak damping, anti-damping and subcritical nonlinearity", "date": "2025", "keywords": "damping; inequality; t t; \u2212 \u222b; \u2223\u2223\u2223; \u2225vt\u2225pvt; \u222b t; \u222b \u03c9", "summary": "+ \u222b T 0 Im(t)dt \u2264 C(R) {\u222b T 0 \u2225\u03b9t(t)\u22252dt+ k \u222b T 0 (\u2225wt\u2225pwt \u2212 \u2225vt\u2225pvt, \u03b9t)dt + k \u222b T 0 |(\u2225wt\u2225pwt \u2212 \u2225vt\u2225pvt, \u03b9)|dt+ \u222b T 0 \u2225\u2207\u03b9\u22252dt+ \u222b T 0 dt \u222b T t \u2225\u2207\u03b9(\u03c4)\u22252d\u03c4 + \u222b T 0 dt \u222b T t \u2225\u2207\u03b9(\u03c4)\u2225\u2225\u03b9t(\u03c4)\u2225d\u03c4 + \u2223\u2223\u2223 \u222b T 0 (N (\u03b9t), \u03b9t)dt \u2223\u2223\u2223+ \u2223\u2223\u2223 \u222b T 0 (N (\u03b9t), \u03b9)dt \u2223\u2223\u2223 + \u2223\u2223\u2223 \u222b T 0 dt \u222b T t (N (\u03b9t), \u03b9t)d\u03c4 \u2223\u2223\u2223+ \u2223\u2223\u2223 \u222b T 0 (g(w)\u2212 g(v), \u03b9t)dt \u2223\u2223\u2223+ \u2223\u2223\u2223 \u222b T 0 (g(w)\u2212 g(v), \u03b9)dt \u2223\u2223\u2223 + \u2223\u2223\u2223 \u222b T 0 dt \u222b T t (g(w)\u2212 g(v), \u03b9t(\u03c4))d\u03c4 \u2223\u2223\u2223}, \u2200T \u2265 + \u222b T 0 dt \u222b T t (N (\u03b9t), \u03b9t)d\u03c4 \u2264 C {\u222b T 0 \u2225\u03b9t\u22252dt+ k \u222b T 0 (\u2225wt\u2225pwt \u2212 \u2225vt\u2225pvt, \u03b9t)dt + k \u222b T 0 |(\u2225wt\u2225pwt \u2212 \u2225vt\u2225pvt, \u03b9)|dt+ \u2223\u2223\u2223 \u222b T 0 ((m(\u2225\u2207w\u22252)\u2212m(\u2225\u2207v\u22252))\u2206v, \u03b9t)dt \u2223\u2223\u2223 + \u2223\u2223\u2223 \u222b T 0 ((m(\u2225\u2207w\u22252)\u2212m(\u2225\u2207v\u22252))\u2206v, \u03b9)dt \u2223\u2223\u2223+ \u2223\u2223\u2223 \u222b T 0 m\u2032(\u2225\u2207w\u22252)\u2225\u2207\u03b9\u22252(\u2206w,wt)dt \u2223\u2223\u2223 + \u2223\u2223\u2223 \u222b T 0 dt \u222b T t ((m(\u2225\u2207w\u22252)\u2212m(\u2225\u2207v\u22252))\u2206v, \u03b9t)d\u03c4 \u2223\u2223\u2223 + \u2223\u2223\u2223 \u222b T 0 dt \u222b T t m\u2032(\u2225\u2207w\u22252)\u2225\u2207\u03b9\u22252(\u2206w,wt)d\u03c4 \u2223\u2223\u2223 + \u2223\u2223\u2223 \u222b T 0 (N (\u03b9t), \u03b9t)dt \u2223\u2223\u2223+ \u2223\u2223\u2223 \u222b T 0 (N (\u03b9t), \u03b9)dt \u2223\u2223\u2223 + \u2223\u2223\u2223 \u222b T 0 dt \u222b T t (N (\u03b9t), \u03b9t)d\u03c4 \u2223\u2223\u2223+ \u2223\u2223\u2223 \u222b T 0 (g(w)\u2212 g(v), \u03b9t)dt \u2223\u2223\u2223 + \u2223\u2223\u2223 \u222b T 0 (g(w)\u2212 g(v),", "mime": "application/pdf"}, {"id": "ejde-126", "words": "5765", "extension": ".pdf", "flesch": "75", "author": "Song, Yingwei; Zhang, Tie; Li, Jinpeng", "title": "Dynamical behavior in a reaction-diffusion system with prey-taxis", "date": "2022", "keywords": "prey", "summary": "[(p(u) u v \u2212 p(u) u v\u2217 ) + (p(u) u v\u2217 \u2212 p(u\u2217) u\u2217 v\u2217 )]} dx + \u222b \u2126 [ A\u03c3(v \u2212 v\u2217) ( \u2212 v u + v\u2217 u \u2212 v\u2217 u + v\u2217 u\u2217 )] dx = \u222b \u2126 [ 1 p(u) ( gu(\u03be)\u2212 v\u2217 d du (p(u) u ) Define a Lyapunov function E(t) = \u222b \u2126 (\u222b u u\u2217 \u03be \u2212 u\u2217 \u03bep(\u03be) d\u03be +A \u222b v v\u2217 \u03b7 \u2212 v\u2217 \u03b7 d\u03b7 )", "mime": "application/pdf"}, {"id": "ejde-1261", "words": "9017", "extension": ".pdf", "flesch": "69", "author": "Wang, Shuna; Liu, Jiang; Fang, Jun; Lin, Xiaojie", "title": "Traveling waves of a diffusive modified Leslie-Gower model with chemotaxis", "date": "2025", "keywords": "equilibrium; existence; leslie; model; r1+b1r2; r1k; subsystem", "summary": "Similarly, for r2V \u2212 U \u2212 k \u2265 0, if U \u2265 U\u2217, we obtain r2V\u0307 \u2212 U\u0307 = \u2212a1U(1\u2212 b1U \u2212 r1V ) = \u2212a1U(1\u2212 b1U \u2212 r1 U + k r2 ) = a1U r2 r2 \u2212 r1k + k(r1 + b1r2) 1 + b1k r1 + b1r2 ] = \u2212a1b1(r2 \u2212 r1k) r1 + b1r2 \u2212 a2 < 0.", "mime": "application/pdf"}, {"id": "ejde-127", "words": "12073", "extension": ".pdf", "flesch": "91", "author": "Ding, Hang; Zhou, Jun", "title": "Global solutions and blow-up for a Kirchhoff-type problem on a geodesic ball of the Poincare ball model", "date": "2022", "keywords": "i(u0; j(u0; q+1; time; \u2016u\u201622", "summary": "\u2212 a\u2016u\u20162 \u2212 b\u2016u\u20164. d\u03c4 \u2212 2(q + 1) (\u222b t 0 (u\u03c4 , u) d\u03c4 )2 \u2265 (q \u2212 3)b 2C4 2 Q(t)(Q\u2032(t))2 \u2212 (q + 1)\u2016u0\u201622Q\u2032(t)\u2212 2(q + 1)J(u0)Q(t). (4.30)", "mime": "application/pdf"}, {"id": "ejde-1270", "words": "31306", "extension": ".pdf", "flesch": "88", "author": "Conlon, Joseph G.; Dabkowski , Michael", "title": "Properties of the Dirichlet Green's function for linear diffusions on a half line", "date": "2025", "keywords": "a(s; a(t; c3 t; c5 t; constant; function; solution; t f0(x; t s; t t; t \u03c4; y t; \u03c4\u2217\u03b5", "summary": "= \u2212min \u03c4>T \u03c4 \u2212 T 2\u03c4T [ y+ \u03c4x (T \u2212 \u03c4) ]2 = \u2212 1 2T [ \u22122xy+min \u03b1>1 {\u03b1x2+y2/\u03b1} ] . P ( \u03c4\u2217\u03b5,linear,x,T < \u03bdT )}] , (6.65) where we assume y \u2265 C3T 2, \u03b5T \u2264 y2, \u221a \u03b5\u03b4 = \u039by.", "mime": "application/pdf"}, {"id": "ejde-1273", "words": "9167", "extension": ".pdf", "flesch": "85", "author": "Lee, Eun Kyoung; Sim, Inbo; Son, Byungjae", "title": "Solutions to nonlinear elliptic problems with nonhomogeneous operators and mixed nonlocal boundary conditions", "date": "2025", "keywords": "solution", "summary": "Let \u03c3 \u2208 (0, 1] and u \u2208 C[0, 1] be a solution of u = \u03c3T\u03bbu and \u2225u\u2225\u221e \u2265 r\u03bb. Let \u03c4 \u2265 0 and u \u2208 C[0, 1] be a solution of u = T\u03bbu + \u03c4 .", "mime": "application/pdf"}, {"id": "ejde-1276", "words": "12738", "extension": ".pdf", "flesch": "86", "author": "Kim, Yong-Cheol", "title": "Holder regularity of weak solutions to nonlocal p-Laplacian type Schrodinger \u00a0equations with A_1^p-Muckenhoupt potentials", "date": "2025", "keywords": "p q; p\u22121; schro\u0308dinger; y s", "summary": "(2.8) EJDE-2025/83 HO\u0308LDER REGULARITY OF WEAK SOLUTIONS 7 For g \u2208 W s,p(Rn), we consider the convex subsets of Xs,p(\u2126) defined by Xs,p g (\u2126)\u00b1 = {v \u2208 Xs,p(\u2126) : (g \u2212 v)\u00b1 \u2208 Xs,p 0 (\u2126)}, Xs,p g (\u2126) := Xs,p g (\u2126)+ \u2229Xs,p g (\u2126)\u2212 = {v \u2208 Xs,p(\u2126) : g \u2212 v \u2208 Xs,p 0 (\u2126)}. If the nonlocal equation mentioned just in the above is considered for 0 < s < 1, p \u2265 2 and a bounded domain \u2126 \u2282 Rn with C1,1 boundary, then they also established the first fine boundary regularity for its weak solutions in [18], i.e. there exist some \u03b1 \u2208 (0, s] and C > 0 depending only on n, p, s and \u2126 such that\u2225\u2225\u2225 u ds\u2126 \u2225\u2225\u2225 C\u03b1(\u2126) \u2264 C\u2225f\u2225 1 p\u22121 L\u221e(\u2126) for any weak solution u \u2208 W s,p 0 (\u2126) of the nonlocal equation, where d\u2126(x) = dist(x, \u2202\u2126).", "mime": "application/pdf"}, {"id": "ejde-1278", "words": "11786", "extension": ".pdf", "flesch": "76", "author": "Huzak, Renato; Mardesic, Pavao; Resman, Maja; Zupanovic, Vesna", "title": "Reading multiplicity in unfoldings from epsilon-neighborhoods of orbits", "date": "2025", "keywords": "analytic; expansion; function; h(\u03bd; point", "summary": "We consider an analytic germ of a system dx dt = F (x, \u03bd), (1.1) with F real, analytic germ in x and in parameter \u03bd, and with a non-hyperbolic singular point x = 0 at the bifurcation value \u03bd = 0 (i.e. F (0, 0) = 0, Fx(0, 0) We use the name compensator for elementary expressions in variable x and parameter \u03bd, i.e. expressions that cannot be further asymptotically expanded uniformly in \u03bd.", "mime": "application/pdf"}, {"id": "ejde-128", "words": "4286", "extension": ".pdf", "flesch": "82", "author": "Mouhcine, Zakariyae", "title": "Resolvent kernel on H-type groups and a Green kernel for fractional powers of its sub-Laplacian", "date": "2022", "keywords": "groups; kernel", "summary": "= (\u03b6 \u2212 L)\u22121 and the heat T (s) = esL operators [7, p.56] R(\u03b6,L) = \u222b \u221e 0 e\u2212\u03b6sT (s) ds, to find the resolvent kernel associated with the sub-Laplacian L. \u00d7 Rm with the group law (x, u) \u00b7 (y, v) = ( x+ y, u+ v + 1 2 \u3008x, Uy\u3009 ) , with x = (x1, . . .", "mime": "application/pdf"}, {"id": "ejde-1282", "words": "8449", "extension": ".pdf", "flesch": "82", "author": "Chen, Xiao; Zhou, Wenxue", "title": "Three-point integral boundary-value problems for piecewise fractional impulsivedifferential equations with p-Laplacian operator", "date": "2025", "keywords": "fractional; i=1; ti\u22121; \u03b3(\u03b1; \u03c8(1; \u03c8(s", "summary": "The significance of studying fractional impulsive differential equations lies in their extension of classical differential equation theory, their ability to reveal new characteristics of complex systems, their capacity to provide precise models for practical problems, and their promotion of innovation in related mathematical methodologies. [9] Z. Bai; Theory and application of fractional differential equation boundary value problem, Beijing: China Science and Technology Press, 2012.", "mime": "application/pdf"}, {"id": "ejde-1285", "words": "6533", "extension": ".pdf", "flesch": "83", "author": "Herron, Sigifredo; Lopera, Emer ; Sanchez, Diana", "title": "Existence of three positive solutions for a p-sublinear problem\u00a0involving a Schrodinger p-Laplacian type operator", "date": "2025", "keywords": "problem; solutions; theorem", "summary": "We prove the existence of three positive solutions for the problem \u2212\u2206pu+ V (x)\u03c6p(u) = \u03bbf(u), x \u2208 \u2126, u(x) The case \u2126 = BR In this section we prove Theorem 1.3.", "mime": "application/pdf"}, {"id": "ejde-129", "words": "6514", "extension": ".pdf", "flesch": "81", "author": "Tordecilla, Jesus Alberto Leon", "title": "Existence of solutions to nonlocal elliptic problems with singular and combined nonlinearities", "date": "2022", "keywords": "problem", "summary": "m0 \u2264M(\u2016vn\u20162H1 0 (\u2126) ) \u2264 m\u221e and since vn > 0, then by taking \u00b5 = \u03bbm\u22121 \u221e we find that \u2212\u2206vn \u2265 \u00b5vqn, x \u2208 \u2126, vn > 0, x \u2208 \u2126, vn = 0, x \u2208 \u2202\u2126. Thus, by defining zn = \u00b5 1 1\u2212q vn we deduce that \u2212\u2206 ( zn \u00b5 1 1\u2212q ) we mean a function u \u2208 H1 0 (\u2126) such that u > 0 in \u2126 and \u2212M (\u222b \u2126 |\u2207u|2 )\u222b \u2126 \u2207u\u2207\u03c6 = \u03bb \u222b \u2126 (a(x)u\u2212\u03b3 + uq)\u03c6+ \u222b \u2126 f(u)\u03c6 = 0 for all \u03c6 \u2208 H1 0 (\u2126).", "mime": "application/pdf"}, {"id": "ejde-1293", "words": "11716", "extension": ".pdf", "flesch": "85", "author": "Chen, Zilin; Yang, Yang", "title": "Normalized solutions for fractional Schrodinger-Choquard systems with Sobolev critical coupled nonlinearity", "date": "2025", "keywords": "critical; lemma", "summary": "If N > 4s, it is easy to check that N + \u03b1 + p(2s\u03b4p,s \u2212 N) < They mainly focused on the L2-subcritical case, and then obtained the existence of normalized positive ground state solution for any 0 < \u03b2 < \u03b20.", "mime": "application/pdf"}, {"id": "ejde-1298", "words": "6223", "extension": ".pdf", "flesch": "78", "author": "Hong, Hakho", "title": "Local solutions for a Brinkman equation coupled with heat-convective and concentration-diffusive equations and a volumetric mass source", "date": "2025", "keywords": "brinkman; system", "summary": "Assume (1.3), (1.4) and Q0(w\u0304, \u03b8\u0304) = 0, S(w\u0304, \u03b8\u0304) = 0, Q1(w\u0304, \u03b8\u0304) = 0. (1.9) 4 H. HONG EJDE-2025/23 Suppose that the initial data \u03c10,u0, \u03c6i0 satisfy (\u03c10 \u2212 \u03c1\u0304,u0,w0 \u2212 w\u0304, \u03b80 \u2212 \u03b8\u0304) \u2208 HN (R3), inf x\u2208R3 \u03c10(x) > 0, inf x\u2208R3 w0(x) > 0, inf x\u2208R3 \u03b80(x) > 0 (1.10) for an integer N \u2265 3. (1.16) Setting \u03c6 = \u03c1\u2212 \u03c1\u0304, m = w \u2212 w\u0304, \u03b6 = \u03b8 \u2212 \u03b8\u0304, and using assumption (1.9), we rewrite system (1.1)1, (1.15)1, (1.1)3, (1.16) as follows: \u03c6t + \u03c1\u0304divu+ u \u00b7 \u2207\u03c6\u2212\u2207wQ0(w\u0304, \u03b8\u0304) \u00b7m\u2212Q\u2032 0\u03b8(w\u0304, \u03b8\u0304)\u03b6 = G1(\u03c6,u,m, \u03b6), ut \u2212 \u00b5 \u03c1\u0304 \u2206u\u2212 \u00b5+ \u03bb \u03c1\u0304 \u2207divu+ 1 \u03b1\u03c1\u0304 u+ P\u03c1(\u03c1\u0304, \u03b8\u0304; w\u0304) \u03c1\u0304 \u2207\u03c6 + P\u03b8(\u03c1\u0304, \u03b8\u0304; w\u0304) \u03c1\u0304 \u2207\u03b6 + n\u2211 i=1 Pwi(\u03c1\u0304, \u03b8\u0304; w\u0304) \u03c1\u0304 \u2207mi = G2(\u03c6,u,m, \u03b6), mt \u2212 df\u2206m+ w\u0304 divu\u2212DwS(w\u0304, \u03b8\u0304)m\u2212 S\u2032 \u03b8(w\u0304, \u03b8\u0304)\u03b6 = G3(\u03c6,u,m, \u03b6), \u03b6t + \u03b8\u0304P\u03b8(\u03c1\u0304, \u03b8\u0304; w\u0304) \u03c1\u0304e\u03b8(\u03c1\u0304, \u03b8\u0304) divu = \u03ba \u03c1\u0304e\u03b8(\u03c1\u0304, \u03b8\u0304) \u2206\u03b6 + \u2207wQ1(w\u0304, \u03b8\u0304) \u00b7m+Q\u2032 1\u03b8(w\u0304, \u03b8\u0304)\u03b6 \u03c1\u0304e\u03b8(\u03c1\u0304, \u03b8\u0304) + e(\u03c1\u0304, \u03b8\u0304) \u03c1\u0304e\u03b8(\u03c1\u0304, \u03b8\u0304) ( \u2207wQ0(w\u0304, \u03b8\u0304) \u00b7m+Q\u2032 0\u03b8(w\u0304, \u03b8\u0304)\u03b6 )", "mime": "application/pdf"}, {"id": "ejde-1299", "words": "8625", "extension": ".pdf", "flesch": "79", "author": "Bensalem, Abdelhamid; Salim, Abdelkrim; Benchohra, Mouffak; N'Guerekata, Gaston M.", "title": "Optimal control and \u00a0approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses", "date": "2025", "keywords": "differential; equations; q(\u03b8; \u03b8 \u2208; \u03d1(\u03b8", "summary": "if \u03b8 \u2208 Ik, k \u2208 Nm 0 , \u03d1(\u03b8) = \u03a5k(\u03b8, \u03d1(\u03b8 \u2212 k )), if \u03b8 \u2208 Jk, k \u2208 Nm 1 , \u03d1\u2032(\u03b8) = \u0398k(\u03b8, \u03d1(\u03b8 \u2212 k )), if \u03b8 \u2208 Jk, k \u2208 Nm 1 , \u03d1\u2032(0) = \u03b60 \u2208 H, \u03d1\u2032(0) = \u03b61 \u2208 H. The concept of controllability has long been recognized as having a significant role in engi- neering and mathematical control theory. + \u222b \u03b8 0 \u03a5(\u03b8, \u03b5)\u03d1(\u03b5)d\u03b5+K(\u03b8, \u03d1\u2111(\u03b8,\u03d1\u03b8), (\u03a8\u03d1)(\u03b8)) + Pu(\u03b8), if \u03b8 \u2208 Ik, k \u2208 Nm 0 , \u03d1(\u03b8) = \u03a5k(\u03b8, \u03d1(\u03b8 \u2212 k )), if \u03b8 \u2208 Jk, k \u2208 Nm 1 , \u03d1\u2032(\u03b8) = \u0398k(\u03b8, \u03d1(\u03b8 \u2212 k )),", "mime": "application/pdf"}, {"id": "ejde-130", "words": "6933", "extension": ".pdf", "flesch": "78", "author": "Hasil, Petr; Sisolakova, Jirina; Vesely, Michal", "title": "Oscillation of modified Euler type half-linear differential equations via averaging technique", "date": "2022", "keywords": "equations; lim; linear; log t; t t", "summary": "= 0, (3.1) lim t\u2192\u221e f(t)g2(t) t log t = 0, (3.2) lim t\u2192\u221e f(t)g(t) t = 0, (3.3) ginf := lim inf t\u2192\u221e g(t) > 0. (3.4) Especially, (3.2) and (3.4) give lim t\u2192\u221e f(t)g(t) t log t = 0, (3.5) 6 P. HASIL, J. S\u030cIS\u030cOLA\u0301KOVA\u0301, M. VESELY\u0301 EJDE-2022/41 i.e., lim t\u2192\u221e t log t f(t)g(t) =\u221e. (3.6) \u2212 1 f(t) \u222b t+f(t) t r(\u03c4)| cosp \u03d5(\u03c4)|p d\u03c4 \u2223\u2223\u2223 \u2264 lim sup t\u2192\u221e 1 f(t) \u222b t+f(t) t r(\u03c4) \u2223\u2223 |cosp (ave[\u03d5, f ](t))|p \u2212 | cosp \u03d5(\u03c4)|p \u2223\u2223d\u03c4 \u2264 lim sup t\u2192\u221e 1 f(t) \u222b t+f(t) t r(\u03c4)C |ave[\u03d5, f ](t)\u2212 \u03d5(\u03c4)|d\u03c4 \u2264 lim sup t\u2192\u221e C ( t log t f(t)g(t) max \u03c4\u2208[t,t+f(t)] |\u03d5(\u03c4)\u2212 ave[\u03d5, f ](t)| ) \u00d7 f(t)g2(t) t log t \u00b7 1 f(t)g(t) \u222b t+f(t) t r(\u03c4) d\u03c4 = lim sup t\u2192\u221e C \u00b7\u2206 (\u03d5, ave[\u03d5, f ]) \u00b7 f(t)g2(t) t log t \u00b7 r[f, g], i.e., lim t\u2192\u221e \u2223\u2223\u2223 |cosp (ave[\u03d5, f ](t))|p ave[r, f ](t)", "mime": "application/pdf"}, {"id": "ejde-131", "words": "8152", "extension": ".pdf", "flesch": "82", "author": "Chang, Caihong; Zhang, Zhengce", "title": "Asymptotic behavior of blowup solutions for Henon type parabolic equations with exponential nonlinearity", "date": "2023", "keywords": "2+\u03c3; equations; log; solutions", "summary": "If N > 10 + 4\u03c3, \u2126(\u03be) = C1\u03be q+ + C2\u03be q\u2212 , (3.8) where C1, C2 > 0, and q\u00b1 = 1 2 [ 4\u2212N \u00b1 \u221a (N \u2212 2)(N \u2212 10\u2212 4\u03c3) ] , which are the roots of the quadratic equation q2 + (N \u2212 4)q + (N\u03c3 \u2212 2\u03c3 +N \u2212 1) = 0. = (2 + \u03c3)\u03bb1 |\u03b3+| t+O(1), t\u2192\u221e, (1.11) where \u03b3+ = 1 2 [ 2\u2212N + \u221a (N \u2212 2)(N \u2212 10\u2212 4\u03c3) ] < 0, and \u03bb1 is defined in Lemma 2.5 as the first eigenvalue of an associated linearized problem.", "mime": "application/pdf"}, {"id": "ejde-132", "words": "9457", "extension": ".pdf", "flesch": "81", "author": "Alves, Maria Jose; Assuncao, Ronaldo B.", "title": "Existence of solutions for a problem with multiple singular weighted p-Laplacians and vanishing potentials", "date": "2022", "keywords": "problem; rn p; |x|ap; |x|ap\u2217(a; |x|cq; |x|cq dx; |x|cq\u2217(c; \u222b rn; \u222b |x|>r", "summary": "The Euler-Lagrange energy functional I : E \u2192 R associated with problem (1.1) is defined by I(u) := 1 p \u222b RN |\u2207u|p |x|ap dx+ 1 p \u222b RN P (x)|u|p |x|ap\u2217(a,b) dx + 1 q \u222b RN |\u2207u|q |x|cq dx+ 1 q \u222b RN Q(x)|u|q |x|cq\u2217(c,d) dx\u2212 \u222b RN F (u) dx. + 1 q \u2016u\u2016q1,q \u2212 c0 \u03b8 \u222b RN |u|p\u2217(a,b) |x|bp\u2217(a,b) dx\u2212 1 kp \u2016u\u2016p1,p = (1 p \u2212 1 kp ) \u2016u\u2016p1,p", "mime": "application/pdf"}, {"id": "ejde-133", "words": "6473", "extension": ".pdf", "flesch": "69", "author": "Sapagovas, Mifodijus; Novickij, Jurij; Ciupaila, Regimantas", "title": "Stability analysis of the Peaceman-Rachford method for parabolic equations with nonlocal conditions", "date": "2022", "keywords": "difference; matrix; method; n+1/2", "summary": "The main task of this article is to construct efficient FDM for the two-dimensional parabolic equation (1.1) with nonlocal boundary condition (1.2). We consider an efficient finite difference method solving of two- dimensional parabolic equations with nonlocal conditions.", "mime": "application/pdf"}, {"id": "ejde-1332", "words": "13038", "extension": ".pdf", "flesch": "85", "author": "Nam, Bui Duc; Nghia, Bui Dai; Tuan, Nguyen Anh", "title": "Mild solutions to Love-type equations on R^2", "date": "2025", "keywords": "equation; k(\u03be2; solution; \u03b7)|2; \u03b72)s; \u03b72)s t", "summary": "Let s \u2264 \u03b8 and \u03b7, d \u2265 0 such that 0 \u2264 d + s \u2212 \u03b8 \u2264 \u03b7 \u2264 d. Suppose that G(0) = 0 and \u2225G(w1)\u2212G(w2)\u2225H\u03b7(R2) \u2264 C\u2225w1 \u2212 w2\u2225Hd(R2), for all w1, w2 \u2208 Hd(R2). = 1 2\u03c0 \u222b\u222b R2 cos (\u221a \u03be2 + \u03b72 1 + k(\u03be2 + \u03b72) t ) a\u0302(\u03be, \u03b7)eix\u03be+iy\u03b7 d\u03be d\u03b7.", "mime": "application/pdf"}, {"id": "ejde-134", "words": "11632", "extension": ".pdf", "flesch": "75", "author": "Kostic, Marko", "title": "Multi-dimensional c-almost periodic type functions and applications", "date": "2022", "keywords": "bohr; c)-almost; function; periodic; recurrent", "summary": "We will always assume henceforth that BX = X, i.e., that for each x \u2208 X there exists B \u2208 B such that x \u2208 B. Further on, there exists B \u2208 B such that x \u2208 B", "mime": "application/pdf"}, {"id": "ejde-1344", "words": "10893", "extension": ".pdf", "flesch": "82", "author": "Zhou, Yao; Liu, Hongliang", "title": "Upper semicontinuity of uniform attractors for singular perturbed second order nonautonomous delay lattice systems", "date": "2025", "keywords": "attractors; lattice; sup; systems", "summary": "+ \u222b t t\u2212\u03d1 \u2225u\u0307\u03f5(r)\u22252dr \u2264 \u03d1K\u03033(\u03f5, q1), t \u2208 R. EJDE-2025/64 ATTRACTORS FOR DELAY LATTICE SYSTEMS 15 Then for t \u2208 R, \u03f5 \u2208 (0, \u03f5], we have\u222b t+1 t \u2225u\u0307\u03f5(r)\u22252dr \u2264 K\u03033(\u03f5, q1) + \u03f5\u2225u\u0307\u03f5(t)\u22252 \u2264 K\u03033(\u03f5, q1) + C1(q1) +M1 . In view of [3, 4, 27], for any g \u2208 H(g0), t \u2208 R, {Ag 0,t}t\u2208R is the pullback attractor of {Ug0 (t, \u03c4)}t\u2265\u03c4 and Ag 0,t = {ut|{ut(\u00b7), t \u2208 R} is a complete bounded trajectory of {Ug0 (t, \u03c4)}t\u2265\u03c4} = \u2229r\u22650\u222as\u2265rUg0 (t, t\u2212 s)B0 \u2282 B0 \u2282 \u21132\u03d1. that is, for all g \u2208 H(g0), t \u2208 R, Ag 0,t is compact in \u21132\u03d1; for all t \u2265 \u03c4 \u2208 R, Ug0 (t, \u03c4)A g 0,\u03c4 = Ag0,t; for all B \u2282 B(\u21132\u03d1), lims\u2192+\u221e dh(U g 0 (t, t \u2212 s)B,Ag0,t)", "mime": "application/pdf"}, {"id": "ejde-1351", "words": "10251", "extension": ".pdf", "flesch": "81", "author": "Zhang, Zujin; Yuan, Weijun; Yao, Zhengan", "title": "Stability of Leray weak solutions to 3D Navier-Stokes equations", "date": "2025", "keywords": "b\u03070; c \u222b; t s; theorem; \u222b r3; \u222b t", "summary": "[(u \u00b7 \u2207)u] \u00b7 vn} dxd\u03c4 = \u222b t 0 \u222b R3 u \u00b7 \u2202\u03c4vndxd\u03c4 + \u222b R3 u0 \u00b7 vn(0)dx+ \u222b t 0 \u222b R3 f \u00b7 vndxd\u03c4, as well as \u222b R3 v(t) \u00b7 un(t)dx+ \u222b t 0 \u222b R3 {\u2207v : \u2207un + = \u222b t 0 \u03b7n(|\u03c4 \u2212 \u03c3|)u(\u03c3)d\u03c3, vn(\u03c4) = \u222b t 0 \u03b7n(|\u03c4 \u2212 \u03c3|)v(\u03c3)d\u03c3 (0 \u2264 \u03c4 \u2264 t). then un,vn \u2208 C1((0, t); H\u03071(R3)), and we may test (1.1)1 and (1.3)1 by vn and un respectively, and obtain \u222b R3 u(t) \u00b7 vn(t)dx+ \u222b t 0 \u222b R3 {\u2207u : \u2207vn +", "mime": "application/pdf"}, {"id": "ejde-136", "words": "8426", "extension": ".pdf", "flesch": "85", "author": "Qu, Siqi; He, Xiaoming", "title": "Multiplicity of high energy solutions for fractional Schrodinger-Poisson systems with critical frequency", "date": "2022", "keywords": "ds,2(r3; fractional; on(1; poisson; schro\u0308dinger", "summary": "In this article we study the fractional Schro\u0308dinger-Poisson system \u03b52s(\u2212\u2206)su+ V (x)u = \u03c6|u|2 \u2217 s\u22123u, x \u2208 R3, (\u2212\u2206)s\u03c6 = |u|2 \u2217 s\u22121, x \u2208 R3, where s \u2208 (1/2, 1), \u03b5 > 0 is a parameter, 2\u2217s = 6/(3\u22122s) is the critical Sobolev exponent, V \u2208 L 3 2s (R3) is a nonnegative function which may be zero in some region of R3. Introduction In the past decades, the nonlinear Schro\u0308dinger-Poisson system \u2212\u2206u+ V (x)u+K(x)\u03c6u = f(x, u), x \u2208 R3, \u2212\u2206\u03c6 = K(x)u2, x \u2208 R3, (1.1) has been the interesting object for many researcher.", "mime": "application/pdf"}, {"id": "ejde-1361", "words": "9508", "extension": ".pdf", "flesch": "84", "author": "Zhang, Lei; Liu, Lintao; Chen, Haibo", "title": "Minimizers for fractional Schrodinger equations with inhomogeneous perturbation", "date": "2025", "keywords": "fractional; lemma; m p\u22121; p\u22121", "summary": "M \u2212 C5A p+1 M \u03b1\u03032s M \u03b1\u0303 (t+1)[N\u2212(N+2s)(p+1)] M + 4s N(p\u2212 1) Ap+1 M \u03b1\u03032s M a\u2217 (M a\u2217 ) M a\u2217 \u222b RN |\u03be|s|Q\u030c(\u03be)|2d\u03be \u2264 C 1 + C\u0303\u03b1\u0303 \u2212(t+1)(N+4s) M a\u2217 \u03b1\u0303 s(1\u2212t) M \u222b RN (1 + |\u03be|2s)|Q\u030c(\u03be)|2d\u03be \u2264 C(1 + C\u0303\u03b1\u0303 \u2212(t+1)(N+4s) M )\u03b1\u0303 s(1\u2212t) M (3.24) EJDE-2025/59 MINIMIZERS FOR FRACTIONAL SCHRO\u0308DINGER EQUATIONS 11 as M \u2192 \u221e, where Q\u030c denote the Fourier transform of Q. By the Ho\u0308lder inequality, (1.7), (3.18) and (3.20), we obtain that |T4| \u2264 C A2 M \u03b1\u0303 2s M a\u2217 (\u222b RN Q2(x)|(\u2212\u2206)s/2\u03c6(\u03b1\u0303\u2212t\u22121 M x)|2dx )1/2 \u00d7 (\u222b RN \u03c62(\u03b1\u0303\u2212t\u22121 M x)|(\u2212\u2206)s/2Q|2dx )1/2 \u2264 C A2 M \u03b1\u0303 2s M a\u2217 ( C3\u03b1\u0303 \u22122s(t+1) M \u222b RN Q2(x)dx )1/2(\u222b RN |(\u2212\u2206)s/2Q|2dx )1/2 \u2264 C(1 + C\u0303\u03b1\u0303 \u2212(t+1)(N+4s) M )\u03b1\u0303 s(1\u2212t) M as M \u2192 \u221e. (3.25) From the Ho\u0308lder inequality, (1.7), (3.18), (3.20) and (3.21), it follows that |T5| \u2264 C A2 M \u03b1\u0303 2s M a\u2217 (\u222b RN Q2(x)|(\u2212\u2206)s/2\u03c6(\u03b1\u0303\u2212t\u22121 M x)|2dx )1/2 \u00d7 (\u222b RN B2(\u03c6(\u03b1\u0303\u2212t\u22121 M x), Q(x))dx )1/2 \u2264 C(1 + C\u0303\u03b1\u0303 \u2212(t+1)(N+4s) M )\u03b1\u03032s M \u03b1\u0303 \u2212s(t+1) M \u03b1\u0303 \u2212 s(t+1) 2 M \u2264 C(1 + C\u0303\u03b1\u0303 \u2212(t+1)(N+4s) M )\u03b1\u0303 s( 1 2\u2212 3 2 t) M asM \u2192 \u221e. (3.26) Similarly, |T6| \u2264 C A2 M \u03b1\u0303 2s M a\u2217 (\u222b RN \u03c62(\u03b1\u0303\u2212t\u22121 M x)|(\u2212\u2206)s/2Q|2dx )1/2(\u222b RN B2(\u03c6(\u03b1\u0303\u2212t\u22121 M x), Q(x))dx )1/2 \u2264 C(1 + C\u0303\u03b1\u0303 \u2212(t+1)(N+4s) M )\u03b1\u03032s M \u03b1\u0303 \u2212 s(t+1) 2 M \u2264 C(1 + C\u0303\u03b1\u0303 \u2212(t+1)(N+4s) M )\u03b1\u0303 s( 3 2\u2212 1 2 t) M asM \u2192 \u221e. (3.27)", "mime": "application/pdf"}, {"id": "ejde-1369", "words": "13209", "extension": ".pdf", "flesch": "81", "author": "Shen, Liejun; Squassin, Marco", "title": "Concentrating normalized solutions for 2D nonlocal Schrodinger equations with critical exponential growth", "date": "2025", "keywords": "equations; lemma; proof; r(a; solutions; theorem", "summary": "In the spirit of [34], when W\u0304 (x) \u2261 0 for all x \u2208 RN in (1.5), the authors in [39] deduced the existence of nontrivial solutions solutions to the nonlocal problem of Choquard type \u2212\u2206u+ \u03c9u = = |s|p\u22122s for all s \u2208 R, (1.5) is of the form \u2212\u2206u+ u = (|x|\u2212\u00b5 \u2217 |u|p)|u|p\u22122u, x \u2208 RN .", "mime": "application/pdf"}, {"id": "ejde-137", "words": "7766", "extension": ".pdf", "flesch": "81", "author": "Lagha, Aesha; Hattori, Hattori", "title": "Cauchy problems for chemotaxis systems with chemo attractant and repellent", "date": "2022", "keywords": "cauchy; chemotaxis; time; u(t", "summary": "There exists a positive number \u03b50 such that if \u2016(n0 \u2212 n\u221e, u0, c1,0, c2,0)\u2016N \u2264 \u03b50, the Cauchy problem (1.3)-(1.4) has a unique solution (n, u, c1, c2)(t) globally in time which satisfies (n\u2212 n\u221e, u)(t) \u2208 C([0,\u221e);HN (R3)) \u2229 C1([0,\u221e);HN\u22121(R3)), (c1, c2)(t) \u2208 C([0,\u221e);HN (R3)) \u2229 C1([0,\u221e);HN\u22122(R3)) and there are constants \u03bb1 > 0, \u03bb2 > 0, \u03bb3 > 0 and C0 > 0 such that \u2016(n\u2212 n\u221e, u, c1, c2)\u20162N + \u03bb1 \u222b t 0 \u2016\u2207(n\u2212 n\u221e)\u20162N\u22121 + \u03bb2 \u222b t 0 \u2016\u2207(c1, c2)\u20162N + \u03bb3 \u222b t 0 \u2016(u, c1, c2)\u20162N \u2264 C0\u2016(n0 \u2212 n\u221e, u0, c1,0, c2,0)\u20162HN . C\u2016\u2202\u03b1\u03c10\u2016+ C\u2016\u03c1\u2016N \u222b t 0 (\u2016\u2202\u03b1u\u20162 + \u2016\u2202\u03b1\u03c1\u20162)ds + C\u2016u\u2016N \u222b t 0 \u2016\u2202\u03b1\u03c1\u20162ds+ C\u2016u\u2016N \u222b t 0 \u2016\u2202\u03b1u\u20162ds + C\u2016c1\u2016N \u222b t 0 (\u2016\u2202\u03b1u\u20162 + \u2016\u2202\u03b1\u2207c1\u20162)ds + C\u2016c2\u2016N \u222b t 0 (\u2016\u2202\u03b1u\u20162 + \u2016\u2202\u03b1\u2207c2\u20162)ds.", "mime": "application/pdf"}, {"id": "ejde-138", "words": "9106", "extension": ".pdf", "flesch": "88", "author": "Hao, Yu-Cai; Zhang, Guo-Bao", "title": "Stability of bistable traveling wavefronts for a nonlocal dispersal epidemic system", "date": "2022", "keywords": "stability; system; u(x; wavefronts", "summary": "By Lemma 3.1 and the comparison principle, one has max { \u03c6i(\u03b7 \u2212(x, t))\u2212 \u03b4pie\u2212\u03b20t, 0 } \u2264 ui(x, t;\u03d5i) \u2264 min { \u03c6i(\u03b7 +(x, t)) + \u03b4pie \u2212\u03b20t, ki } , i = 1, 2, (3.4) where x \u2208 R, t \u2265 0, and \u03b7\u00b1(x, t) : Hence, combining with (3.3) and (3.4), we obtain \u03c6i(x+ ct)\u2212 \u03b5 2 \u2264 ui(x, t;\u03d5i) \u2264 \u03c6i(x+ ct) + \u03b5 2 , \u2200x \u2208 R, t \u2265 0, i = 1, 2, which implies that \u2016u(\u00b7, t;\u03d5)\u2212 \u03c6(\u00b7+ ct)\u2016 < \u03b5, \u2200t \u2265 0.", "mime": "application/pdf"}, {"id": "ejde-1383", "words": "6762", "extension": ".pdf", "flesch": "75", "author": "Llibre, Jaume; Valls, Claudia", "title": "Global asymptotic stability in quadratic systems", "date": "2025", "keywords": "a01; a10; b01; condition; equilibrium; system; theorem", "summary": "c < (\u2212a01 + b10)/a10 + 2 \u221a \u2212(a210 + a01b10)/a210, (4) a01 > 0, \u22122a01 < a10 < 0, \u2212a01 + 2a10 \u2212 2 \u221a \u22122a01a10 \u2212 a210 < b10 < \u2212a01 + 2a10 + 2 \u221a \u22122a01a10 \u2212 a210, and (b10 \u2212 a01)/a10 \u2212 2 \u221a \u2212(a210 + a01b10)/a210 < 2)XY \u2212 d(b2 \u2212 bcd+ d2)Y 2, Y\u0307 = \u2212(a2b10 \u2212 a(a10 \u2212 b01)c1 \u2212 a01c 2 1)X + (c1(a10b+ a01d) \u2212 a(bb10 + b01d))Y + c1(a 2 \u2212 acc1 + c21)X 2 + (a2d+ 2c21d+ ac1(b\u2212 2cd))XY + d(c1d+ a(b\u2212 cd))Y 2. (3.13) We first impose that system (3.13) can be written in the form (a) of Theorem 2.4, that is, that satisfies abb10 + bb01c1 \u2212 aa10d\u2212 a01c1d = c1(ab\u2212 bcc1 + c1d)", "mime": "application/pdf"}, {"id": "ejde-1385", "words": "7978", "extension": ".pdf", "flesch": "85", "author": "Zheng, Feng-Xia; Li, Hong-Xu", "title": "Almost automorphic solutions to non-autonomous dynamic equations with Stepanov-like almost automorphic forcing terms on time scales", "date": "2025", "keywords": "t+k)t; time", "summary": "\u2208 K for t \u2208 T. By Lemma 3.2, we have f \u2208 SpAAK(T\u00d7X,Y ), and a subsequence {\u03ben}\u221en=1 of {\u03be\u2032n}\u221en=1 and a function f\u0303 such that lim n\u2192\u221e ( 1 K \u222b [t,t+K)T sup x\u2208K \u2225f(s+ \u03ben, x)\u2212 f\u0303(s, x)\u2225p\u2206s )1/p = 0 for t \u2208 T, lim n\u2192\u221e ( 1 K \u222b [t,t+K)T sup x\u2208K \u2225f\u0303(s\u2212 \u03ben, x)\u2212 f(s, x)\u2225p\u2206s )1/p = 0 for t \u2208 T. (3.9) and g is Sp-a.a., for any sequence {\u03be\u2032n}\u221en=1 \u2282 \u03a0, there exist a subsequence {\u03ben}\u221en=1 of {\u03be\u2032n}\u221en=1 and two functions f\u0303 , g\u0303 such that lim n\u2192\u221e f(t+ \u03ben) = f\u0303(t) for t \u2208 T, lim n\u2192\u221e f\u0303(t\u2212 \u03ben) = f(t) for t \u2208 T, (2.2) lim n\u2192\u221e ( 1 K \u222b [t,t+K)T \u2225g(s+ \u03ben)\u2212 g\u0303(s)\u2225p\u2206s )1/p = 0 for t \u2208 T, lim n\u2192\u221e ( 1 K \u222b [t,t+K)T \u2225g\u0303(s\u2212 \u03ben)\u2212 g(s)\u2225p\u2206s )1/p = 0 for t \u2208 T. (2.3)", "mime": "application/pdf"}, {"id": "ejde-1388", "words": "10661", "extension": ".pdf", "flesch": "83", "author": "Zhang, Mingbo", "title": "Approximations of Euler-Peano scheme for reflected stochastic differential equations with non-Lipschitz coefficients", "date": "2025", "keywords": "solution; stochastic; sup; |x|\u2264r; \u03c3(s; \u222b t", "summary": "= \u222b t 0 b(s, x(s, x0))ds+ \u222b t 0 \u03c3(s, x(s, x0))dB(s) + \u03d5(t, x0), t \u2264 T. The uniqueness and continuous dependence with respect to x0 of the solution of equation (1.1) will be presented in Theorem 3.10. In this article we are concerned with the reflected stochastic differential equations (RSDEs) x(t) = x0 + \u222b t 0 \u03c3(s, x(s))dB(s) + \u222b t 0 b(s, x(s))ds+ \u03d5(t), x0 \u2208 D\u0304, \u03d5(t)", "mime": "application/pdf"}, {"id": "ejde-139", "words": "8884", "extension": ".pdf", "flesch": "70", "author": "Alvarez-Caudevilla, Pablo", "title": "Asymptotic behavior of cooperative systems involving p-Laplacian operators", "date": "2022", "keywords": "1,p; eigenvalue; problem; \u2212 \u222b", "summary": "Moreover, \u2126 is a smooth bounded domain of RN , N \u2265 1, with smooth boundary \u2202\u2126, for example of class C2 or Lipschitz. and we denote the open sets/subdomains of \u2126 where the potentials a and d vanish, as \u2126a0 := {x \u2208 \u2126 : a(x)", "mime": "application/pdf"}, {"id": "ejde-1395", "words": "8159", "extension": ".pdf", "flesch": "76", "author": "El Idrissi, Ahmed; Srhiri, Halima; El Boukari, Brahim; El Ghordaf, Jalila", "title": "Local and global solvability of fractional porous medium equations in critical Besov-Morrey spaces", "date": "2025", "keywords": "besov; p p; spaces; \u22122m+n p", "summary": "In fact, if we have p = h, then N\u0307 s p,p,r = B\u0307s p,r. 3. It is important to note that replacing the Lp-norm by the Mp h-norm is not sufficient to ensure a direct transition from Besov spaces to Besov-Morrey spaces.", "mime": "application/pdf"}, {"id": "ejde-140", "words": "7409", "extension": ".pdf", "flesch": "83", "author": "Wang, Ru; Chang, Xiaojun", "title": "Existence of global solutions and blow-up for p-Laplacian parabolic equations with logarithmic nonlinearity on metric graphs", "date": "2022", "keywords": "equations; lemma; log; logarithmic", "summary": "Integrating on (0, t) with t \u2208 (0, T ), by 1 < p < 2 it follows that 1 2 \u222b G |w(t)|2dx \u2264 \u222b t 0 \u222b G ((p\u2212 1) log |w\u0303(s)|+ 1)|w\u0303(s)|p\u22122|w(s)|2 dx ds \u2264 C \u222b t 0 \u222b G |w(s)|2 dx ds for some constant C > 0 independent of u1(t) and u2(t). A function u := u(x, t) is called a weak solution of problem (1.1) on G \u00d7 (0, T\u2217), if u \u2208 L\u221e(0, T\u2217;W 1,p(G)) with ut \u2208 L2(0, T\u2217;L 2(G)) satisfies (1.1) in the distribution sense, i.e.,\u222b G utvdx+ \u222b G |u\u2032|p\u22122u\u2032v\u2032dx+ \u222b G |u|p\u22122uvdx = \u222b G |u|p\u22122uv log |u|dx, for all v \u2208W 1,p(G), a.e. t \u2208 (0, T\u2217), where u(x, 0) = u0(x) \u2208 X0. 4 R. WANG, X. J. CHANG EJDE-2022/51 Our first result is about the existence of a local solution.", "mime": "application/pdf"}, {"id": "ejde-1400", "words": "8217", "extension": ".pdf", "flesch": "81", "author": "Begout, Pascal; Diaz, Jesus Ildefonso", "title": "Title: Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions", "date": "2025", "keywords": "solution", "summary": "If \u2225F\u2225L2(RN ) \u2264 \u03b4 and \u2225F\u2225L\u221e(Kc) \u2264 1 M , then there exists a self-similar solution (u, U) to (1.2) such that u \u2208 C ( (0,\u221e);H2(RN ) ) \u2229 C1 ( (0,\u221e);H1(RN ) ) \u2229 C2 ( (0,\u221e);L2(RN ) ) (2.10) and for any t > 0, suppu(t) is compact. On the other hand, if for some 0 < q \u2264 \u221e, u \u2208 C ( (0,\u221e);Lq(RN ) ) then \u03c6 \u2208 Lq(RN ) and it follows from (2.5) that \u2200t > 0, \u2225u(t)\u2225Lq(RN )", "mime": "application/pdf"}, {"id": "ejde-1401", "words": "4982", "extension": ".pdf", "flesch": "75", "author": "Molica Bisci, Giovanni; De Lima, Henrique; Leite, Ary V. F. ARY V.F.; Velasquez, Marco A. L.", "title": "Complete noncompact and stochastically complete m-quasi Yamabe gradient solitons", "date": "2025", "keywords": "gradient; quasi; riemannian; soliton; yamabe", "summary": "= 1 2 \u2206|\u2207u|2 \u2265 |\u22072u|2 = n m2 (R\u2212 \u03c1)2u2 \u2265 0, implying that R = \u03c1. \u25a1 Proceeding, we will deal with complete noncompact m-quasi Yamabe gradient solitons having exponential volume growth. Now, we are in a position to present our first characterization result related to complete non- compact m-quasi Yamabe gradient soliton.", "mime": "application/pdf"}, {"id": "ejde-141", "words": "14087", "extension": ".pdf", "flesch": "76", "author": "Diaz, Jesus Ildefonso; Shaposhnikova, Tatiana A.; Zubova, Maria N.", "title": "A strange non-local monotone operator arising in the homogenization of a diffusion equation with dynamic nonlinear boundary conditions on particles of critical size and arbitrary shape", "date": "2022", "keywords": "l2(0; operator; problem; solution; t 0; t j; \u03b5\u2212\u03b3 \u222b; \u222b t", "summary": "= \u2212C0g(x, t) + C0\u2202t\u03c6(x, t), y \u2208 \u2202G0, t \u2208 (0, T ), w\u03c6(x, y, 0) = \u03c6(x, 0), y \u2208 \u2202G0, w\u03c6 \u2192 0, |y| \u2192 \u221e. (6.13) We consider the sequence of solutions {w\u03c6,R} to the problems \u2206yw\u03c6,R = 0, y \u2208 T 0 R \\G0, t \u2208 (0, T ), C0\u2202tw\u03c6,R + \u2202\u03bdw\u03c6,R \u2212 C0\u03c3(\u03c6\u2212 w\u03c6,R) Using the maximum principle, we derive the estimate |w\u03c6,R| \u2264 K0R0 |y|n\u22122 , y \u2208 T 0 R \\G0, t \u2208 (0, T ).", "mime": "application/pdf"}, {"id": "ejde-1411", "words": "6587", "extension": ".pdf", "flesch": "88", "author": "Wang, Tao; Tian, Xiaoyu; He, Wenling", "title": "New type of multi-bump solutions for Schrodinger-Poisson systems", "date": "2025", "keywords": "solutions; |p+", "summary": "U pe\u2212x1 ; \u2022 H1(R3) is the usual Sobolev space endowed with inner product (u, v) = \u222b R3(\u2207u\u2207v+uv)dx and norm \u2225u\u22252 = \u222b R3(|\u2207u|2 + u2)dx; \u2022 D1,2(R3) is the completion of C\u221e 0 (R3) with respect to the norm \u2225u\u22252D1,2 = \u222b R3 |\u2207u|2dx; \u2022 Hk and Dk are symmetric Sobolev subspaces defined by Hk By using Ho\u0308lder inequality and Sobolev inequality, we obtain \u2225\u03a6u\u22252D1,2 = \u222b R3 \u03a6uu 2dx \u2264", "mime": "application/pdf"}, {"id": "ejde-142", "words": "6593", "extension": ".pdf", "flesch": "85", "author": "de Paiva, Francisco Odair; Lima, Sandra Machado de Souza; Miyagaki, Olimpio Hiroshi", "title": "Existence of at least four solutions for Schrodinger equations with magnetic potential involving and sign-changing weight function", "date": "2023", "keywords": "problem; solutions", "summary": "[15] Gidas, B.; Nirenberg, L.; Symmetry of positive solutions of nonlinear elliptic equations in RN . [21] Kwong, M. K.; Uniqueness of positive solutions of \u2206u \u2212 u + up = 0 in Rn, Archive for Rational Mechanics and Analysis, 105.3 (1989): 243-266.", "mime": "application/pdf"}, {"id": "ejde-1420", "words": "12965", "extension": ".pdf", "flesch": "78", "author": "Yang, Xin; Zhou, Jueliang", "title": "Classification of boundary-equilibria for two-dimensional continuous piecewise linear systems with two intersecting switching lines", "date": "2025", "keywords": "resp; \u03ba \u2208", "summary": "\u2212a3/a2 > 0, \u2212(a1 \u2212 a4)/a2 > 0 the solution on the x-axis (j) \u2212a3/a2 = 0, \u2212(a1 \u2212 a4)/a2 = 0 the solution outside Q1 (k) \u2212a3/a2 > 0, \u2212(a1 \u2212 a4)/a2 < 0 the solution on the y-axis (l) \u2212a2/a3 = 0, (a1 \u2212 a4)/a3 = 0 D1 1 = ( \u22122a2, a1 \u2212 a4 \u2212 \u221a (a1 \u2212 a4)2 + 4a2a3 ) and D2 1 = ( \u22122a2, a1 \u2212 a4 + \u221a (a1 \u2212 a4)2 + 4a2a3 ) . When the separatrix with the characteristic direction D2 1 is located in Q1 except the x-axis (resp. on the x-axis, outside Q1), we obtain H2 1 := \u22122a2 ( a1 \u2212 a4 + \u221a (a1 \u2212 a4)2 + 4a2a3 ) > (resp.", "mime": "application/pdf"}, {"id": "ejde-143", "words": "4962", "extension": ".pdf", "flesch": "81", "author": "Wu, Yingzhu; Yu, Yuanhong; Xiao , Jinsen", "title": "Oscillation for second order nonlinear differential equations with a sub-linear neutral term", "date": "2022", "keywords": "differential; oscillation", "summary": "Then a1/\u03b3(t)(\u2212z\u2032(t)) is an increasing function and thus z\u2032(s) \u2264 ( a(t) a(s) )1/\u03b3z\u2032(t), s \u2265 t \u2265 t2. > 0 for all t \u2265 t1.", "mime": "application/pdf"}, {"id": "ejde-1438", "words": "19255", "extension": ".pdf", "flesch": "81", "author": "Zheng, Yanzhi; Yin, Jingxue; Ji, Shanming", "title": "Complete classification of self-similar solutions for singular polytropic filtration equations", "date": "2025", "keywords": "equation; filtration; m(p\u2212; near; solutions; \u03b4 m", "summary": "\u2264 \u2212m1\u2212p ( a\u2212M \u2212 N \u2212 \u03b1 N (a+M) ) = 2m(1\u2212 2m)(m\u03b1\u2212 \u03b4 + 3m\u03b4) 3(1\u2212m)(m\u03b1\u2212 \u03b4 + 2m\u03b4)2 \u00b7 C2 2,0u(\u03b1) v(\u03b1\u2217) , C2,1 = \u2212 (1\u2212m)(1\u2212 2m) 2m3(p\u2212 1) \u03b42\u2212p\u2113\u22121+ 1 m\u2212p = \u2212 2m2(1\u2212 2m) (1\u2212m)(m\u03b1\u2212 \u03b4 + 2m\u03b4)2 C2 2,0u 2(\u03b1) v(\u03b1) , C1,2 = \u2212 (2\u2212 p)(1\u2212m) 2m2(p\u2212 1)2 \u03b43\u22122p\u21131+ 1 m\u22122p, \u03b4C1,2 = \u2212 2(2\u2212 p)m3 (1\u2212m)(m\u03b1\u2212 \u03b4 + 2m\u03b4)2 C2 2,0u 3(\u03b1) v(\u03b1) , C0,3 = \u2212 (2\u2212 p)(3\u2212 2p) 6m(p\u2212 1)3 \u03b44\u22123p\u21133+ 1 m\u22123p, \u03b42C0,3 = \u2212 2m4(2\u2212 p)(3\u2212 2p) 3(1\u2212m)2(m\u03b1\u2212 \u03b4 + 2m\u03b4)2 C2 2,0u 4(\u03b1) v(\u03b1) , \u03b4B2 = \u2212 (2\u2212 p)m2 (1\u2212m)(m\u03b1\u2212 \u03b4 + 2m\u03b4) C2,0u 3(\u03b1) v(\u03b1) .", "mime": "application/pdf"}, {"id": "ejde-144", "words": "4897", "extension": ".pdf", "flesch": "79", "author": "Chen, Feng", "title": "Periodic solutions of stochastic Volterra equations", "date": "2022", "keywords": "equations; k(t; periodic; solutions", "summary": "We prove the existence of periodic solutions in distribution of stochastic Volterra equations. This paper concerns the existence of periodic solutions in the distribution of stochastic Volterra equations.", "mime": "application/pdf"}, {"id": "ejde-1440", "words": "5515", "extension": ".pdf", "flesch": "83", "author": "Tu, Kun; Ding, Hui-Sheng", "title": "Shadowing properties of evolution equations with exponential trichotomy on Banach spaces", "date": "2025", "keywords": "+ \u221e; s t; t t; y(r; \u222b +", "summary": "+ \u222b t 0 T (t, r)(y\u2032(r)\u2212A(r)y(r))dr, t \u2208 R+. + \u222b t 0 T (t, r)f(r, x(r))dr, t \u2208 R+, and x(t)\u2212 y(t)", "mime": "application/pdf"}, {"id": "ejde-145", "words": "4125", "extension": ".pdf", "flesch": "80", "author": "Liu, Zhenhai; Papageorgiou, Nikolaos S.", "title": "Double phase equations with an indefinite concave term", "date": "2022", "keywords": "1,\u03b7", "summary": "In (3.4) we choose h = un \u2212 u \u2208 W 1,\u03b7 0 (\u2126), pass to the limit as n \u2192 +\u221e and use (3.16). Introduction Let \u2126 \u2286 RN be a bounded domain with a Lipschitz boundary \u2202\u2126. In this paper we study the double phase problem \u2212\u2206a pu(z)\u2212\u2206qu(z)", "mime": "application/pdf"}, {"id": "ejde-1452", "words": "11460", "extension": ".pdf", "flesch": "91", "author": "Zhang, Xiaohui; Xu, Xian", "title": "Multiple solutions for parametric weighted (p,q)-equations", "date": "2025", "keywords": "1,p; f(z; inty; lemma; \u2225v\u2225x", "summary": "0textfor a.a.z \u2208 \u2126, all x \u2a7e 0. If hypotheses (H0), (H1) hold, \u03bb \u2208 L \u2212, v\u03bb \u2208 S\u2212 \u03bb , and \u00b5 \u2208 (0, \u03bb), then \u00b5 \u2208 L \u2212 and there exists v\u00b5 \u2208 S\u2212 \u00b5 \u2286 intY (\u2212P1) such that v\u03bb \u2a7d v\u00b5. Lemma 2.13.", "mime": "application/pdf"}, {"id": "ejde-1454", "words": "9601", "extension": ".pdf", "flesch": "68", "author": "Chavez, Alan; Aragones, Nelson; Zavaleta, Ulices; Pinto, Manuel", "title": "Compact almost automorphic dynamics of linear non-autonomous differential equationswith exponential dichotomy and of delayed biological models", "date": "2025", "keywords": "function; lim; n\u2192+\u221e; solution", "summary": "If x(\u00b7) is defined on the interval [t0 \u2212 \u03c4, \u03c3] with t0, \u03c3 \u2208 R, then the function xt \u2208 C([\u2212\u03c4, 0],R) is defined by xt(\u03b8) := x(t + \u03b8) for all \u03b8 \u2208 [\u2212\u03c4, 0] and t0 \u2264 t \u2264 \u03c3. Let C+ be the cone of non-negative functions in C([\u2212\u03c4, 0],R), i.e., C+ = {\u03d5 \u2208 C([\u2212\u03c4, 0],R) : \u03d5(t) \u2265 0}, and define the set C+ 0", "mime": "application/pdf"}, {"id": "ejde-1457", "words": "10727", "extension": ".pdf", "flesch": "79", "author": "Yayla, Sema", "title": "Structure and stability of global attractors for a Cahn-Hilliard tumor growth model with chemotaxis", "date": "2025", "keywords": "lemma; theorem", "summary": "\u2212 \u03c7\u03c3\u0304\u03c7, (4.8) \u27e8\u03c3\u0304\u03c7 t, \u03be\u27e9 + \u27e8\u2207\u03c3\u0304\u03c7,\u2207\u03be\u27e9 = \u03c7\u27e8\u2207\u03d5\u0304\u03c7,\u2207\u03be\u27e9 \u2212 \u27e8p(\u03d5\u03c7)(\u03c3\u0304\u03c7 \u2212 \u03c7\u03d5\u0304\u03c7 \u2212 \u00b5\u0304\u03c7), \u03b7\u27e9, (4.9) for all \u03b7, \u03be \u2208 H1(\u2126). = \u03d5\u03c7 \u2212 \u03d5\u2217, \u03c3\u0304\u03c7 := \u03c3\u03c7 \u2212 \u03c3\u2217 and \u00b5\u0304\u03c7 := \u00b5\u2212 \u00b50, we obtain from (2.9) that \u27e8\u03d5\u0304\u03c7 t, \u03b7\u27e9 + \u27e8\u2207\u00b5\u0304\u03c7,\u2207\u03b7\u27e9 = \u27e8p(\u03d5\u03c7)(\u03c3\u0304\u03c7 \u2212 \u03c7\u03d5\u0304\u03c7 \u2212 \u00b5\u0304\u03c7), \u03b7\u27e9, (4.7) \u00b5\u0304\u03c7 = \u2212\u2206\u03d5\u0304\u03c7 + \u03a8\u2032(\u03d5\u03c7) \u2212 \u03a8\u2032(\u03d5\u2217)", "mime": "application/pdf"}, {"id": "ejde-146", "words": "7861", "extension": ".pdf", "flesch": "82", "author": "Idczak, Dariusz", "title": "A parabolic bipolynomial fractional Dirichlet-Laplace problem", "date": "2022", "keywords": "b;x; function", "summary": "We know that d dt (f(t), \u03c8(t))X = (f \u2032(t), \u03c8(t))X + (f(t), \u03c8\u2032(t))X (2.6) for t \u2208 = f \u2032(t)\u03d5(t) + f(t)\u03d5\u2032(t) for t \u2208 (a, b), and any function \u03d5 \u2208 C\u221ec (a, b;R).", "mime": "application/pdf"}, {"id": "ejde-1469", "words": "6208", "extension": ".pdf", "flesch": "72", "author": "Almutairi, Sarah; Saoudi, Kamel", "title": "Combined effects of critical Hardy-Sobolev exponent and singular nonlinearities in nonlocal problems with variable weights", "date": "2025", "keywords": "problem; solution; |x|t", "summary": "\u25a1 References [1] K. Kefi, M. Kratou, K. Saoudi; Combined effects of critical and singular nonlinearities in fractional problems, submitted (2025). The third result concerns the regularity of weak solutions of problem (1.1).", "mime": "application/pdf"}, {"id": "ejde-147", "words": "9864", "extension": ".pdf", "flesch": "85", "author": "Wang, Lixia", "title": "Localized nodal solutions for semiclassical nonlinear Kirchhoff equations", "date": "2022", "keywords": "h1(r3; lemma; solutions; |\u2207vj; \u222b r3", "summary": "For every 1 \u2264 i \u2264 mj, v\u0303i is a nontrivial solution of \u2212 (a+ bAj)\u2206v + V (yij)v = |v|p\u22122v, v \u2208 H1(R3), (4.13) where yij = lim\u03b5\u21920 \u03b5y i j,\u03b5 \u2208 \u039b\u0304; (iii) For any 2 < q < 6, lim \u03b5\u21920 \u2016vj,\u03b5 \u2212 v\u03030 \u2212 mj\u2211 i=1 v\u0303i(\u00b7 \u2212 yij,\u03b5)\u2016Lq(R3) = 0. (4.14) Proof. Since vj,\u03b5, v\u03030 and v\u03031 solves (2.4), (4.12), and (4.13) with i = 1 respectively, we have \u2212 a\u2206v2 j,\u03b5 \u2212 b \u222b R3 |\u2207vj,\u03b5|2dx\u2206v2 j,\u03b5 \u2212 b (\u222b R3 |\u2207vj,\u03b5|2 \u2212Aj ) \u2206v\u03030 \u2212 b (\u222b R3 |\u2207vj,\u03b5|2 \u2212Aj ) \u2206v\u03031 + \u03be\u03b5\u03c7\u03b5v 2 j,\u03b5 + \u03be\u03b5\u03c7\u03b5v\u03030 + \u03be\u03b5\u03c7\u03b5v\u03031 + V (\u03b5x)v2 j,\u03b5 + (V (\u03b5x)\u2212 V (0))v\u03030 + (V (\u03b5x)\u2212 V (yij))v\u03031(\u00b7 \u2212 y1 j,\u03b5) = |vj,\u03b5|p\u22122vj,\u03b5 \u2212 |v\u03030|p\u22122v\u03030 \u2212 |v\u03031|p\u22122v\u03031(\u00b7 \u2212 y1 j,\u03b5).", "mime": "application/pdf"}, {"id": "ejde-1474", "words": "2912", "extension": ".pdf", "flesch": "77", "author": "Chen, Zhuoru; Wang, Taige; Xie, Xiangfei", "title": "Bilinear estimates posed in finite domains in 2D and 3D", "date": "2025", "keywords": "estimates", "summary": "\u2207v(s)\u2225ds \u2264 C \u222b T 0 \u2225\u2207u(s)\u2225(\u2225\u2207v(s)\u2225+ \u2225\u2207v(s)\u22251/2\u2225Av(s)\u22251/2)ds whence \u222b T 0 \u2225u(s) \u00b7 Second, on \u222b T 0 \u2225\u2207(u(s) \u00b7", "mime": "application/pdf"}, {"id": "ejde-1475", "words": "9766", "extension": ".pdf", "flesch": "67", "author": "Girg, Petr; Kotrla, Lukas; Svandova, Anezka", "title": "p-Laplacian in phenomenological modeling of flow in porous media and CFD simulations", "date": "2025", "keywords": "flow; fracture; groundwater; law; media; model; network; rock; solution; water", "summary": "In Section 2, we present several mathemat- ical models of groundwater flow in phreatic aquifers and related models used in EJDE-2022/2025/CONF/26 FLOW IN POROUS MEDIA AND CFD SIMULATIONS 181 irrigation and drainage. [24, 50], despite their limited well yields due to water flow occurring only in cracks and fractures.", "mime": "application/pdf"}, {"id": "ejde-1476", "words": "7906", "extension": ".pdf", "flesch": "72", "author": "Tumanyan, Ani", "title": "Normal solvability and Fredholm properties for special classes of hypoelliptic operators", "date": "2025", "keywords": "operator; p q; q \u2208", "summary": "We also provide applications to the smoothness of solutions, index invariance on the scale, and spectral properties of such operators. Isomorphic characteristics for quasielliptic op- erators with constant coefficients on a special scale of weighted spaces have been derived in the works of Demidenko (see [10, 11]), and such operators have been 2020 Mathematics Subject Classification.", "mime": "application/pdf"}, {"id": "ejde-1477", "words": "9351", "extension": ".pdf", "flesch": "84", "author": "Zhang, Zhenbu", "title": "Traveling wave solutions for an epidemic model", "date": "2025", "keywords": "j=1; m+1; model; speed; ui(z; wave", "summary": "The differential susceptibility epidemic model \u2202I \u2202t = dIIxx + \u03b7\u03b2I l\u2211 j=1 \u03b1jSj \u2212 (\u00b5+ \u03b3)I x \u2208 R, t > 0, \u2202Si \u2202t = diSixx + \u00b5piS 0 \u2212 \u03b7\u03b2\u03b1iISi \u2212 \u00b5Si, x \u2208 R, t > 0, i = 1, 2, . . u = (u1, u2, . . .", "mime": "application/pdf"}, {"id": "ejde-148", "words": "7586", "extension": ".pdf", "flesch": "82", "author": "Ye, Xiaobing; Wang, Liangchen", "title": "Boundedness and asymptotic stability in a chemotaxis model with indirect signal production and logistic source", "date": "2022", "keywords": "tmax; \u222b \u03c9", "summary": "Testing the first equation in (1.1) by lnu+ 1 and integrating we have d dt \u222b \u2126 u lnu = \u222b \u2126 (lnu+ 1)\u2206u\u2212 \u222b \u2126 (lnu+ 1)\u2207 \u00b7 (u\u2207v) + \u00b5 \u222b \u2126 (lnu+ 1)u(1\u2212 u) = \u2212 \u222b \u2126 |\u2207u|2 u + \u222b \u2126 \u2207u \u00b7 \u2207v + \u00b5 \u222b \u2126 (lnu+ 1)u(1\u2212 u) \u2264 \u2212 \u222b \u2126 u\u2206v + \u00b5 \u222b \u2126 (lnu+ 1)u(1\u2212 u) \u2264 \u222b \u2126 uw + \u00b5 \u222b \u2126 u+ \u00b5 \u222b \u2126 u lnu\u2212 \u00b5 \u222b \u2126 u2 \u2212 \u00b5 \u222b \u2126 u2 lnu (3.2) for all t \u2208 (0, Tmax). [1, 8], testing the first equation of (1.1) by up\u22121(p \u2265 2) and integrating by parts over \u2126, using (4.22) and Young\u2019s inequality we have 1 p d dt \u222b \u2126 up + (p\u2212 1) \u222b \u2126 up\u22122|\u2207u|2 + \u00b5 \u222b \u2126 up+1 = (p\u2212 1) \u222b \u2126 up\u22121\u2207u \u00b7 \u2207v + \u00b5 \u222b \u2126 up \u2264 c2(p\u2212 1) \u222b \u2126 up\u22121|\u2207u|+ \u00b5(p\u2212 1) \u222b \u2126 up \u2264 p\u2212 1 2 \u222b \u2126 up\u22122|\u2207u|2 + (c22 2 + \u00b5 ) (p\u2212 1) \u222b \u2126 up (4.23) for all t \u2208 (0, Tmax).", "mime": "application/pdf"}, {"id": "ejde-1487", "words": "9222", "extension": ".pdf", "flesch": "79", "author": "Chen, Jiaxue; Li, Yeping; Yin, Rong", "title": "Zero-viscosity-capillarity limit for the contact discontinuity for the 1-D full compressible \u00a0Navier-Stokes-Korteweg equations", "date": "2025", "keywords": "c \u222b; cd y; sup; ucd; v cd; y +; y v; \u03b8cd; \u03c4 \u03c40; \u03c40 \u222b; \u03c40\u2264\u03c4\u2264\u03c4; \u222b \u03c4", "summary": "y \u03b6y \u2212 \u03bd ( 1 \u0398CD ) y \u03b6y (\u03b6yyv \u2212 \u03b6y\u03d5y)\u2212 (\u03b6yV CD y + \u03d5y\u0398 CD y ) + (\u0398CD yy v \u2212\u0398CD y V CD y ) v2 + \u03bd ( 1 \u0398CD ) y \u03b6y \u0398CD yy V CD \u2212\u0398CD y V CD y (V CD)2 \u2212 ( \u03bd 1 \u0398CD \u0398CD yy V CD \u2212\u0398CD y V CD y (V CD)2 ) y \u03b6y \u2212 (\u03c8y + UCD y )2 v ( 1 \u0398CD ) y \u03b6y + (UCD y )2 V CD ( 1 \u0398CD ) y \u03b6y \u2212 \u03c82 y + 2\u03c8yU CD y v\u0398CD \u03b6yy \u2212 \u03bb(\u03c8y + UCD y ) (5(\u03d5y + V CD y )2 2v6 \u2212 \u03d5yy + V CD yy v5 )( 1 \u0398CD ) |\u03c8y\u03d5yy\u03b6yy|+ |\u03d53y\u03c8yy|+ |\u03c8y\u03d5 2 y\u03b6yy|, J2 = |\u03d5y\u03c8y(\u0398 CD y + V CD y )|+ |\u03b6y\u03c8y(V CD y +\u0398CD y )|+ |\u03d52yUCD y |+ |\u03b62yUCD y | + |\u03b6y\u03d5yUCD y |+ |\u03d5y\u03c8y(U CD y V CD y + UCD yy )|+ |\u03b62y\u0398CD y V CD y | + |\u03b6y\u03d5y((\u0398CD y )2 +\u0398CD yy +\u0398CD y V CD y + (UCD y )2)|+ |\u03c8y\u03b6yU CD y \u0398CD y | + |\u03d5y\u03c8y(V CD y V CD yy + (V CD y )3 + V CD yyy )|+ |\u03c8y\u03b6y\u0398 CD y ((V CD y )2 + V CD yy )| + |\u03d5y\u03b6y(UCD y V CD y \u0398CD y + UCD y (V CD y )2 + UCD y V CD yy )|, J3 = |\u03d5\u03c8y(V CD y \u0398CD y +\u0398CD yy + (V CD y )2 + V CD yy )|+ |\u03b6\u03c8y((V CD y )2 + V CD yy )| + |(\u03d5+ \u03b6)\u03b6yU CD yy |+ |\u03d5\u03c8y(V CD y UCD yy + UCD yyy + (V CD y )2UCD y + V CD yy", "mime": "application/pdf"}, {"id": "ejde-149", "words": "6933", "extension": ".pdf", "flesch": "84", "author": "Fu, Song-Ren; Ning, Zhen-Hu", "title": "Stabilization of the critical nonlinear Klein-Gordon equation with variable coefficients on R^3", "date": "2022", "keywords": "equation; \u222b r3; \u222b t", "summary": "dt+ \u222b T 0 \u222b \u2126 a(x)utH(u) dx dt+ \u222b T 0 \u222b R3 a(x)utH(u) dx dt + 3 2 \u222b T 0 \u222b R3 (u2 t \u2212 |\u2207gu|2g \u2212 u2 \u2212 1 3 u6) dx", "mime": "application/pdf"}, {"id": "ejde-1499", "words": "6238", "extension": ".pdf", "flesch": "73", "author": "Zhai, Xiaoping", "title": "Linear stability of the Couette flow for non-isentropic compressible fluids", "date": "2025", "keywords": "compressible; couette; flow; linear; stability; \u2202tp", "summary": "Integration in x equations in (1.15), one infer that \u2202t\u03c10 = \u2212\u03b10, \u2202t\u03b10 = \u2212 1 \u03b3M2 \u2202yy\u03c10 \u2212 1 \u03b3M2 \u2202yy\u03b80 + \u03bd\u2202yy\u03b10, \u2202t\u03c90 = \u03b10, \u2202t\u03b80 = \u2212(\u03b3 \u2212 1)\u03b10. (2.1) From (2.1), we can further get \u03b10 satisfies the damped wave equations \u2202tt\u03b10 \u2212 \u03bd\u2202t\u2202yy\u03b10 \u2212 1 M2 \u2202yy\u03b10 = 0, in R, (2.2) and \u03c10 + \u03b80 satisfies the wave equation \u2202tt(\u03c10 + \u03b80)\u2212 1 M2 \u2202yy(\u03c10 + \u03b80) (2.15) 8 X. ZHAI EJDE-2025/107 From the equations in (2.10) and definitions of Z1 and Z2, a simple computations gives \u2202tZ1 = \u2212\u2202tm m Z1 \u2212 1 4 \u2202tp p Z1 \u2212 1 M p1/2Z2, \u2202tZ2 = \u2212 (\u2202tm m + \u03bdp ) Z2", "mime": "application/pdf"}, {"id": "ejde-15", "words": "12143", "extension": ".pdf", "flesch": "78", "author": "Remy, Pascal", "title": "Gevrey regularity of the solutions of inhomogeneous nonlinear partial differential equations", "date": "2023", "keywords": "gevrey; \u03b3(1", "summary": "Then, denoting by C(a, b) the domain C(a, b) = {(x, y) \u2208 R2 : x \u2264 a and y \u2265 b} for any (a, b) \u2208 R2, the Newton polygon at t = 0 of the operator (3.7) is defined as the convex hull of C(\u03ba,\u2212\u03ba) \u22c3\u22c3 i\u2208K \u22c3 q\u2208Qi C(\u03bb(q) + i, vi,q,p\u2217 \u2212 i), where \u03bb(q) = q1 + \u00b7 \u00b7 \u00b7+ qn denotes the length of q = (q1, . . . Let i \u2208 K, q \u2208 Qi, p \u2208 Pi,q, j \u2265 vi,q,p, and `0, `1, . . .", "mime": "application/pdf"}, {"id": "ejde-150", "words": "7466", "extension": ".pdf", "flesch": "85", "author": "Marcial, Marcos Roberto; Miyagaki, Olimpio H.; Pereira, Gilberto A.", "title": "Topological structure of the solution set for a fractional p-Laplacian problem with singular nonlinearity", "date": "2022", "keywords": "solution", "summary": "We consider the convex, closed subset of I\u039b \u00d7 C(\u2126) given by G\u039b := { (\u03bb, u) \u2208 I\u039b \u00d7 C(\u2126) : \u03bb \u2208 I\u039b, u \u2264 u \u2264 u and u = 0 on \u2126c } . In \u00d7BRn : u \u2264 u \u2264 u, u = 0 on \u2202\u2126 } , where Rn = R\u039bn .", "mime": "application/pdf"}, {"id": "ejde-151", "words": "5538", "extension": ".pdf", "flesch": "83", "author": "Wang, Lixiong; Chen, Haibo; Yang, Liu", "title": "Ground state solutions for fractional p-Kirchhoff equation", "date": "2022", "keywords": "p2s; y|n+ps; |x\u2212; \u222b rn", "summary": "14 L. WANG, H. CHEN, L. YANG EJDE-2022/61 [11] X. Huang, Y. Zhang; Existence and uniqueness of minimizers for L2-constrained problems related to fractional Kirchhoff equation. [16] Z. Liu, M. Squassina, J. Zhang; Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension, NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 4, Paper No. 50, 32.", "mime": "application/pdf"}, {"id": "ejde-1515", "words": "16085", "extension": ".pdf", "flesch": "87", "author": "Nunez-Chavez, Miguel R.", "title": "Controllability under positivity constraints for non-linear and non-local parabolic PDEs", "date": "2025", "keywords": "control; controllability; dx\u2032; function; lemma; linear; proof; solution; system; t t; z(x; \u2212 y", "summary": "\u2212 y \u2208 C2+ 1 2 ,1+ 1 4 (QT ) \u2282 C([0, T ];L2(\u2126)) and as (z(0)\u2212 y(0), \u03c60) Multiplying by \u2212\u2206(y \u2212 y) in (3.3) and integrating in \u2126, we obtain\u222b \u2126 (y \u2212 y)t(\u2212\u2206(y \u2212 y))", "mime": "application/pdf"}, {"id": "ejde-152", "words": "10339", "extension": ".pdf", "flesch": "83", "author": "Wang, Zhenqiang", "title": "Higher differentiability for solutions to nonhomogeneous obstacle problems with 1", "date": "2022", "keywords": "c \u222b; n\u22122\u03b1; n\u22122\u03b1 dx; n\u22122\u03b1 n; \u222b b2r; \u222b br; \u222b \u03c9", "summary": "[ 1 + \u222b B2R |F | np n\u22122\u03b1 dx+ \u222b B2R |D\u03c8| np n\u22122\u03b1 dx+ ( \u222b B2R |Du|pdx) n n\u22122\u03b1 ]n\u22122\u03b1 n + c \u222b BR |\u03c4hVp(D\u03c8)|2 |h|2\u03b1 dx+ c|h|(\u03b1+1)(1\u2212\u03b2) (\u222b BR (\u03b9k(x) + \u03b9k(x+ h))n/\u03b1dx )\u03b1/n \u00d7 [ 1 + \u222b B2R |F | np n\u22122\u03b1 dx+ \u222b B2R |D\u03c8| np n\u22122\u03b1 dx+ (\u222b B2R |Du|pdx ) n n\u22122\u03b1 ]n\u22122\u03b1 n + c|h|p( \u222b BR |DF | np n\u22122\u03b1 dx) Suppose that there exists \u03c1 \u2208 (0, R) and M > 0 such that n\u2211 s=1 \u222b B\u03c1 |\u03c4s,hF (x)|pdx \u2264Mp|h|p, for all h with |h| < R\u2212\u03c1 2 .", "mime": "application/pdf"}, {"id": "ejde-1521", "words": "13496", "extension": ".pdf", "flesch": "81", "author": "Song, Xiao; Wang, Chenhua; Wang, Xiaojie; Xu, Fuyi", "title": "Global unique solution for 3D incompressible inhomogeneous magneto-micropolar equations with discontinuous density", "date": "2025", "keywords": "global; hj)\u2225l2 t; l2 t; t b\u0307; t uj; \u2212 \u222b; \u222b r3", "summary": "[Dt; curl]DtujDtwj dx. (3.38) 14 X. SONG, C. WANG, X. WANG, F. XU EJDE-2025/58 Multiplying (??) by t2 and then integrating over [0, t] give rise to 2\u2225t\u2207Dt(\u03c9j , Hj)\u22252L\u221e t (L2) + 2\u2225tdivDt\u03c9j\u22252L\u221e t (L2) + \u2225t(\u221a\u03c1D2 t uj , \u221a \u03c1D2 t\u03c9j , D 2 tHj)\u22252L2 t (L 2) + \u2225t\u2207Dtuj\u22252L\u221e t (L2) + \u2225tdivDtuj\u22252L\u221e t (L2) + \u2225t(curlDtuj \u2212 2Dtwj)\u22252L\u221e t (L2) \u2272 \u2225 \u221a t\u2207Dt(uj , \u03c9j , Hj)\u22252L2 t (L 2) + \u2225 \u221a tdivDt\u03c9j , Dt\u03c9j\u22252L2 t (L 2) + \u222b t 0 \u03c42 \u222b R3 \u2207Dt\u03c0jD 2 t uj dx d\u03c4 + \u222b t 0 \u03c42 \u222b R3 \u2207DtHj \u00b7 [Dt;\u2207]DtHj dx d\u03c4 + \u222b t 0 \u03c42 \u222b R3 \u2207Dtuj \u00b7", "mime": "application/pdf"}, {"id": "ejde-1529", "words": "6160", "extension": ".pdf", "flesch": "86", "author": "Fan, Zian", "title": "Normalized ground state solutions for Kirchhoff equation with subcritical or critical perturbation", "date": "2025", "keywords": "m(c; p\u03b3p", "summary": "Lately in the aid of subcritical approximation method, we prove the existence of normalized ground state solutions for q = 2\u2217 for any \u03b7 > 0 . If q = 2\u2217, by using the definition of S0 we obtain\u222b R3 |u|2 \u2217 dx \u2264 S \u22122\u2217/2 0 \u2225\u2207u\u22252 \u2217 2 . (2.2) Since the embedding H1(R3) \u2192 Lj(R3)(2 < j \u2264 2\u2217) is continuous, then we deduce that Iq \u2208 C1(E,R).", "mime": "application/pdf"}, {"id": "ejde-153", "words": "12742", "extension": ".pdf", "flesch": "80", "author": "Adhikari, Dhruba R.; Aryal, Ashok; Bhatt, Ghanshyam; Kunwar, Ishwari J.; Puri, Rajan; Ranabhat, Min", "title": "Solvability of inclusions involving perturbations of positively homogeneous maximal monotone operators", "date": "2022", "keywords": "degree; monotone; operator", "summary": "For a sequence {xn} in X and x0 \u2208 X, we denote by xn \u2192 x0 and xn \u21c0 x0 the strong convergence and weak convergence, respectively. We may assume that there exist x0 \u2208 X and w0 \u2208 X\u2217 such that xn \u21c0 x0 in X and A\u03d5tnxn \u21c0 w0 in X\u2217.", "mime": "application/pdf"}, {"id": "ejde-1531", "words": "13930", "extension": ".pdf", "flesch": "84", "author": "Ha, Tae Gab", "title": "Global solutions and blow-up for wave equations with variable coefficients and boundary supercritical source", "date": "2025", "keywords": "energy; equation; source; t s; wave; \u03b3+2,\u03b31; \u03c1+1; \u03c1+2; \u222b t; \u222b \u03b31", "summary": "Indeed, considering w = u\u03b7m in (3.1) and then integrating over (0, T ), we have\u222b T 0 \u27e8u\u03b7mtt , u\u03b7m\u27e9 dt+ \u222b T 0 \u00b5(t)\u2225 |\u2207gu \u03b7m|g\u222522 dt+ \u03b7 \u222b T 0 \u27e8u\u03b7mt , u\u03b7m\u27e9\u03931 dt 10 T. G. HA EJDE-2025/104 + \u222b T 0 \u27e8q(u\u03b7mt ), u\u03b7m\u27e9\u03931 dt\u2212 \u222b T 0 \u27e8h(u\u03b7m), u\u03b7m\u27e9\u03931 dt = \u222b T 0 \u27e8f, u\u03b7m\u27e9 dt. Next, considering w = u\u03b7mt in (3.1) and then integrating over (0, T ), we have\u222b T 0 \u27e8u\u03b7mtt , u \u03b7m t \u27e9 dt+ \u222b T 0 \u00b5(t) \u222b \u2126 \u27e8\u2207gu \u03b7m,\u2207gu \u03b7m t \u27e9g dx dt+ \u03b7 \u222b T 0 \u2225u\u03b7mt \u222522,\u03931 dt + \u222b T 0 \u27e8q(u\u03b7mt ), u\u03b7mt \u27e9\u03931 dt\u2212 \u222b T 0 \u27e8h(u\u03b7m), u\u03b7mt \u27e9\u03931 dt = \u222b T 0 \u27e8f, u\u03b7mt \u27e9 dt. From (3.14)-(3.18) and (3.22), we arrive at lim m\u2192\u221e,\u03b7\u21920 \u222b T 0 \u27e8q(u\u03b7mt ), u\u03b7mt \u27e9\u03931 dt = \u222b T 0 \u27e8\u03c8, ut\u27e9\u03931 dt.", "mime": "application/pdf"}, {"id": "ejde-1534", "words": "7543", "extension": ".pdf", "flesch": "85", "author": "Lu, Can; Wang, Liangwei; Yin, Jingxue; Zhou, Meiling", "title": "Complicated asymptotic behavior of solutions to doubly nonlinear diffusionequation in unbounded spaces", "date": "2025", "keywords": "equation; m(p\u22121)\u22121; y\u03c3(rn", "summary": "Let p p\u22121 \u2264 \u03c3 < p m(p\u22121)\u22121 , if 0 \u2264 u0 \u2208 L\u221e(\u03c1\u03c3). (3.10) EJDE-2025/108 DOUBLY NONLINEAR DIFFUSION EQUATIONS 7 For any \u03b5 > 0, and the following assumptions are satisfied 0 \u2264 u0 \u2208 Y\u03c3(RN ), then there exists a constant R1 > 1 > 0, It follows that for |x| > R1, (1 + |x|2)\u2212\u03c3/2 u0(x) < \u03b5 2 .", "mime": "application/pdf"}, {"id": "ejde-154", "words": "6063", "extension": ".pdf", "flesch": "82", "author": "Qin, Liuna; Xiao, Changguo; Zhang, Yinghui", "title": "Optimal decay rates for higher-order derivatives of solutions to 3D compressible Navier-Stokes-Poisson equations with external force", "date": "2022", "keywords": "decay; equations; navier; poisson; stokes; system", "summary": "For T > 0, let (\u03c1 \u2212 \u03c1\u0303, u, \u03c6 \u2212 \u03c6\u0303)(x, t) be a solution of (1.1) in [0, T ] and introduce E(T ) Then there exists \u03b4 > 0 such that if E(T ) + \u03b51 \u2264 \u03b4, (1.6) then the following a-priori estimate holds \u2016(\u03c1\u2212 \u03c1\u0303, u,\u2207\u03c6\u2212\u2207\u03c6\u0303)(\u00b7, t)\u20162H2 + \u222b t 0 \u2016(\u03c1\u2212 \u03c1\u0303,\u2207u,\u22072\u03c6\u2212\u22072\u03c6\u0303)(\u00b7, s)\u20162H2ds \u2264 C\u2016(\u03c10 \u2212 \u03c1\u0303, u0)\u20162H2 , (1.7) for any t \u2208", "mime": "application/pdf"}, {"id": "ejde-1543", "words": "8062", "extension": ".pdf", "flesch": "79", "author": "Fernandes, Juliana; Maia, Liliane", "title": "Nehari manifold for degenerate logistic parabolic equations", "date": "2025", "keywords": "solutions", "summary": "u|t=0 = u0(x), x \u2208 \u2126, (1.1) where \u2126 is an open smooth bounded domain in RN , N \u2265 2, \u03bb is a real positive parameter, 1 < \u03bd < 2\u2217 \u2212 1, where 2\u2217 = +\u221e if N = 2, or 2\u2217 = 2N/(N \u2212 2) if N \u2265 3, and b is a continuous function satisfying b(x) \u2264 0 and b(x) = 0 in a smooth proper subdomain \u21260 of \u2126, with positive Lebesgue measure and smooth boundary.", "mime": "application/pdf"}, {"id": "ejde-155", "words": "6051", "extension": ".pdf", "flesch": "78", "author": "Di Fazio, Giuseppe; Fanciullo, Maria Stella; Zamboni, Piero", "title": "Boundary regularity for strongly degenerate operators of Grushin type", "date": "2022", "keywords": "b3r; p\u22121", "summary": "In this way we can define infS u, supS u and oscS u. Now, let Br be a ball centered at x0 \u2208 \u2202\u2126 and u \u2208 H1,p v (\u2126 \u2229B4r, w) we set u\u0303(x) = { min{u,m} if x \u2208 \u2126 \u2229B4r m if x \u2208 Rn \\ (\u2126 \u2229B4r) where m = inf\u2202\u2126\u2229B4r This is a kind of generalization of the [1, 4] to quasilinear elliptic equations.", "mime": "application/pdf"}, {"id": "ejde-157", "words": "9378", "extension": ".pdf", "flesch": "78", "author": "Guo, Cuiping; Guo, Shangjiang", "title": "Stationary and oscillatory dynamics of Nicholson's blowflies equation with Allee effect", "date": "2022", "keywords": "solutions; state; steady; u(t; u\u22172(p", "summary": "Nonconstant steady states Steady state solutions of (1.2) satisfy d\u2206u(x)\u2212 u(x) + f(u(x)) In particular, we present the bifurcation direction for each branch of steady state solutions and periodic solutions.", "mime": "application/pdf"}, {"id": "ejde-1570", "words": "9361", "extension": ".pdf", "flesch": "81", "author": "Wei, Qifan; Zhang, Xuemei", "title": "Existence and multiplicity of solutions to triharmonic problems", "date": "2025", "keywords": "g(x; order; solutions; theorem", "summary": "In particular, by using a variant version of the mountain pass lemma, Hu-Wang [29] obtained the existence of nontrivial solutions for the following fourth-order problem \u22062u+ \u03b1\u2206u = f(x, u) in \u2126, u = \u2206u = 0 on \u2202\u2126, (1.3) where \u22062(u) = \u2206(\u2206u) stands for the biharmonic operator, \u2126 \u2282 RN (N > 4) is a smooth bounded domain, and \u03b1 < \u00b51 is a parameter, where \u00b51 is the first eigenvalue of (\u2212\u2206) in H1 0 (\u2126). [37] studied the fourth-order problem \u22062u+ \u03b2\u2206u = a(x)|u|s\u22122u+ f(x, u) in \u2126, u = \u2206u = 0 on \u2202\u2126, (1.4) where \u2126 \u2282 RN (N > 4) is a smooth bounded domain, \u03b2 < \u00b51, a(x) \u2208 L\u221e(\u2126), s \u2208 (1, 2) and f \u2208 C(\u2126\u0304 \u00d7 R,R).", "mime": "application/pdf"}, {"id": "ejde-1576", "words": "13702", "extension": ".pdf", "flesch": "83", "author": "Neto, Antonio Francisco", "title": "New approach to the Lagrange-Burmann theorem via omega calculus and applications", "date": "2025", "keywords": "function; omega; proof; theorem; \u03bb \u03c9", "summary": "= \u03c41 \u2212 \u03bb \u2126 = \u03bb ln ( 1\u2212 \u03b6 G(\u03bb) ) , (7.7) In this case \u03b1 = 0, \u03b2 = 1, and \u03b3 = 0 = \u03c41 (and hence \u03b4 = 0).", "mime": "application/pdf"}, {"id": "ejde-158", "words": "4325", "extension": ".pdf", "flesch": "77", "author": "Pinelas, Sandra; Tunc, Osman", "title": "Solution estimates and stability tests for nonlinear delay integro-differential equations", "date": "2022", "keywords": "differential; equations; i=1; integro; stability", "summary": ", l. Hence, W \u2032(\u00b7) \u2264 \u22122y m\u2211 i=1 fi(t, x, y)\u2212 2yg(x, y) + [ n\u2211 i=1 (\u03b1i\u03c4i) + l\u2211 i=1 (diri\u03c4i) + n\u2211 i=1 (\u03b3i\u03c4i) ] y2 + (\u03b11 + d1r1 \u2212 \u03b31) \u222b t t\u2212\u03c41 y2(s) ds+ (\u03b12 + d2r2 = \u222b t t\u2212 1 4 1 1 + t4 + s2 x\u2032(s)", "mime": "application/pdf"}, {"id": "ejde-1586", "words": "9664", "extension": ".pdf", "flesch": "83", "author": "Meng, Fanmeng; Zhou, Xian-Feng", "title": "Decay estimates and extinction properties of parabolic equations with classical and fractional time derivatives", "date": "2025", "keywords": "fractional; |u(x", "summary": "We say u(x, t) vanishes in finite time if there exists a constant T > 0 such that u(x, t) \u2261 0 in \u2126 for t \u2265 T . = ( Y (0)\u2212 m0 2\u03bb1C\u2217 t ) > 0, 0 < t < T, Y (t) \u2261 0, t \u2265 T, (5.16) where T = 2\u03bb1C\u22c6Y (0) m0 .", "mime": "application/pdf"}, {"id": "ejde-1588", "words": "9900", "extension": ".pdf", "flesch": "78", "author": "Lee, Mikyoung; Ok, Jihoon", "title": "L^q-regularity estimates for double obstacle problems \u00a0with quasilinear operators and Schrodinger-type lower order terms", "date": "2025", "keywords": "estimates; obstacle; \u03c9r v; \u2212 \u222b; \u222b \u03c9r", "summary": "We deal with the function u \u2208 A0(\u2126) that satisfies the variational inequality\u222b \u2126 a(x,Du) \u00b7D(u\u2212 \u03c6) dx+ \u222b \u2126 V |u|s\u22122u(u\u2212 \u03c6) dx \u2264 \u222b \u2126 |F |p\u22122F \u00b7D(u\u2212 \u03c6) dx (1.7) for all \u03c6 \u2208 A0(\u2126). \u00b7D(v1 \u2212 v2)+ dx \u2264 0.", "mime": "application/pdf"}, {"id": "ejde-159", "words": "9910", "extension": ".pdf", "flesch": "87", "author": "Lou, Zhaowei; Sun, Yingnan", "title": "A KAM theorem for higher dimensional reversible nonlinear Schrodinger equations", "date": "2022", "keywords": "j k; kam; zd1; zd2; \u03c3 j", "summary": "We introduce the Banach space `\u03c1I of all 4 Z. LOU, Y. SUN EJDE-2022/69 complex sequences z = (zj)j\u2208Zd\\I with \u2016z\u2016\u03c1 = \u2211 j\u2208Zd\\I e|j|\u03c1|zj | <\u221e, where |j| = \u221a |j1|2 + \u00b7 \u00b7 \u00b7+ |jd|2. = r 2\u03bd+3 , r\u03bd+1 = r\u03bd \u2212 2\u03b4\u03bd , r0 = r, \u03b5\u03bd+1 = c\u03b3\u22125\u03b4\u22121 \u03bd K5\u03c4+19 \u03bd \u03b55/3 \u03bd + \u03b57/6 \u03bd , \u03b50 = \u03b5, e\u2212K\u03bd\u03b4\u03bd = \u03b51/2 \u03bd , \u03b7\u03bd = \u03b51/3 \u03bd , s\u03bd+1 = 1 4 \u03b7\u03bds\u03bd , s0 = s, L\u03bd+1 = L\u03bd + \u03b5\u03bd , L0 = L, \u03c1\u03bd = \u03c1(1\u2212 \u03bd+1\u2211 i=2 2\u2212i). 5.5.1.", "mime": "application/pdf"}, {"id": "ejde-1590", "words": "7684", "extension": ".pdf", "flesch": "85", "author": "Nghia, Le Trung", "title": "Hardy operators and commutators on generalized central function spaces", "date": "2025", "keywords": "hap\u2032,r\u2032; hardy; r \u03c6; spaces; \u02d9cmo", "summary": "In this article, we study the boundedness of operators of Hardy type on generalized central function spaces, such as the generalized central Hardy space HAp,r \u03c6 (Rn), the generalized central Morrey space M\u0307p,r \u03c6 (Rn), and the generalized central Campanato space \u02d9CMO p,r \u03c6 (Rn), with p \u2208 (1,\u221e), and \u03c6(t) : (0,\u221e) \u2192 (0,\u221e). Furthermore, there exists a constant C > 0 depend- ing on n, p such that \u2225b\u2225 \u02d9CMO p,r \u2264 C\u2225[b,H\u2217]\u2225M\u0307p,r \u03c6 \u2192M\u0307p,r \u03c6 .", "mime": "application/pdf"}, {"id": "ejde-1597", "words": "7391", "extension": ".pdf", "flesch": "79", "author": "Sun, Jinyi; Mai, Yuanwei; Yang, Minghua", "title": "Well-posedness of generalized magnetohydrodynamic equations in variable Lebesgue spaces", "date": "2025", "keywords": "2\u03b1\u22121; spaces; variable", "summary": "This article concerns the well-posedness of the generalized magnetohydrodynamic equations in variable Lebesgue spaces. By using some basic properties of variable Lebesgue spaces and decay estimates of the fractional heat kernel, we prove the existence of local and global solutions to the generalized magnetohydrodynamic equations in two different types of variable Lebesgue spaces.", "mime": "application/pdf"}, {"id": "ejde-1599", "words": "6899", "extension": ".pdf", "flesch": "68", "author": "Wang, Tiantian; Fan, Hongxia", "title": "Topological properties of the solution set and T-controllability for\u00a0second-order neutral evolution equations with delay", "date": "2025", "keywords": "controllability; equations; set; solution", "summary": "= I; (iii) C(t)x is continuous in t on R for each fixed x \u2208 X. Define the associated sine family {S(t) : t \u2208 R} by S(t)x = \u222b t 0 C(s)xds, x \u2208 X, t \u2208 R. The infinitesimal generator of a strongly continuous cosine family {C(t) : t \u2208 R} is the operator A : D(A) \u2282 X \u2192 X defined by Ax = d2 dt2 C(t)x |t=0, x \u2208 D(A), where D(A) = {x \u2208 X : C(\u00b7)x \u2208 C2(R,X)}. +Bu(t) + f(t, x(a(t)), x[h(x(t), t)]), t \u2208 J", "mime": "application/pdf"}, {"id": "ejde-160", "words": "5143", "extension": ".pdf", "flesch": "83", "author": "Chen, Shaohua; Xu, Runzhang; Yang, Chao", "title": "Improved blowup time estimates for fourth-order damped wave equations with strain term and arbitrary positive initial energy", "date": "2022", "keywords": "blowup; finite; time", "summary": "(2.3) Then \u03a6(t) blows up in finite time T , where T < \uf8f1\uf8f2\uf8f3 1 2\u03b8\u2212\u03b3 ln ( (2\u03b8\u2212\u03b3)\u03a6(0) (\u03b1\u22121)\u03a6\u2032(0)\u2212\u03b8\u03a6(0) + 1 ) if 2\u03b8 > \u03b3, \u03a6(0) (\u03b1\u22121)\u03a6\u2032(0)\u2212\u03b3\u03a6(0)/2 if 2\u03b8 \u2264 \u03b3. (2.4) Proof. = 2.4 and \u00b5 = 0.3, then (2.2) is satisfied and the solution blows up with blowup time T \u2217 < 2.37 based on (2.4).", "mime": "application/pdf"}, {"id": "ejde-1606", "words": "11510", "extension": ".pdf", "flesch": "76", "author": "Zhu, Xi; Zhu, Min; Wang, Ying; Wang, Ke", "title": "Wave-breaking for two-component Fornberg-Whitham systems with dissipation", "date": "2025", "keywords": "blow; bs\u22121 q; equation; system; wave; \u2225\u03c10\u2225l1", "summary": "By Cantor\u2019s diagonalization ar- gument, for any test function \u03c6 \u2208 C\u221e c (R), the quantities \u2225\u03c6un \u2212 \u03c6u\u2225Bs\u22121 q,r and \u2225\u03c6\u03b7n \u2212 \u03c6\u03b7\u2225Bs\u22122 q,r converge uniformly to 0 on [0, T ] as n \u2192 \u221e. Using the Fatou property of Besov spaces from Lemma 2.3(vi), for all t \u2208 Let s \u2208 R and 1 \u2264 q, r \u2264 \u221e.", "mime": "application/pdf"}, {"id": "ejde-161", "words": "12535", "extension": ".pdf", "flesch": "82", "author": "Zhao, Qiulan; Cheng, Hongbiao; Li, Xinyue; Li, Chuanzhong", "title": "Integrable nonlinear perturbed hierarchies of NLS-mKdV equation and soliton solutions", "date": "2022", "keywords": "darboux; ejde-2022/71; equation; hierarchy; i=0; mkdv; nls; nonlinear; n\u22121; solutions; transformation", "summary": "(3.6) When m = 2, setting \u03b5 = 1, we obtain pt = \u03b1qxx \u2212 \u03b1hxq \u2212 2\u03b1hpx \u2212 \u03b1h2q + \u03b1q(p2 + q2) + \u03b1q((qpx \u2212 pqx) + 2\u03b1h(p2 + q2)), qt = \u2212\u03b1pxx \u2212 \u03b1hxp\u2212 2\u03b1hpx + \u03b1h2p\u2212 \u03b1p(p2 + q2) 2\u03b1(qrx \u2212 rqx) + 4\u03b1h(p2 + q2)\u2212 \u03b2h(q2 \u2212 p2) + 2h2), st = \u2212\u03b1rxx \u2212 \u03b1pxx + \u03b2pxx + 2\u03b1qhx + 4\u03b1hqx \u2212 \u03b1shx \u2212 \u03b1hs\u03b2qhx \u2212 2\u03b2hqx \u2212 \u03b1hsx \u2212 4\u03b1h2p+ 2\u03b1h2r + 2\u03b2h2p+ 2\u03b1p2r", "mime": "application/pdf"}, {"id": "ejde-162", "words": "8645", "extension": ".pdf", "flesch": "77", "author": "Lopes, Juliana Honda; Planas, Gabriela", "title": "Existence of solutions for a non-isothermal Navier-Stokes-Allen-Cahn system with thermo-induced coefficients", "date": "2022", "keywords": "cahn; existence; l2(0; navier; stokes; system", "summary": "We note that (2.3) implies the existence of some positive constants Ci, i = 1, 2, 3 such that \u2212 C1 \u2264 F \u2032\u2032(s), \u2212C2 \u2264 F (s) \u2264 F \u2032(s)s+ C3 for all s \u2208 R, (2.5) where F (s) = \u222b Then \u03c61 \u2212 \u03c62 solves (\u03c61 \u2212 \u03c62)t + u \u00b7 \u2207(\u03c61 \u2212 \u03c62) = \u2207 \u00b7 (\u03b5(\u03b8)\u2207(\u03c61 \u2212 \u03c62))\u2212 1 \u03b5(\u03b8) (F \u2032(\u03c61)\u2212 F \u2032(\u03c62)) together with \u2202 \u2202\u03b7 (\u03c61 \u2212 \u03c62) = 0 on \u2202\u2126\u00d7 (0, T ) and (\u03c61 \u2212 \u03c62)(0) = 0 in \u2126. Multiplying the above equation by \u03c61 \u2212 \u03c62 and integrating in \u2126, we see 1 2 d dt \u2016\u03c61 \u2212 \u03c62\u20162 + \u03b50\u2016\u2207(\u03c61 \u2212 \u03c62)\u20162 \u2264 \u2212 ( 1 \u03b5(\u03b8) (F \u2032(\u03c61)\u2212 F \u2032(\u03c62)), \u03c61 \u2212 \u03c62 ) \u2264 C\u2016F \u2032(\u03c61)\u2212 F \u2032(\u03c62)\u2016\u2016\u03c61 \u2212 \u03c62\u2016 \u2264 C\u2016\u03c61 \u2212 \u03c62\u20162, EJDE-2022/72 NON-ISOTHERMAL NAVIER-STOKES-ALLEN-CAHN SYSTEM 9 where we used that \u2207 \u00b7 u = 0, the Mean Value Theorem for F \u2032 and the fact that F \u2032\u2032 is bounded.", "mime": "application/pdf"}, {"id": "ejde-163", "words": "7823", "extension": ".pdf", "flesch": "78", "author": "Zhao, Xutong; Zhou, Mingjun; Zhou, Qian", "title": "Asymptotic behavior of solutions to coupled porous medium systems with boundary degeneracy", "date": "2022", "keywords": "m\u22121)/m; s)ds", "summary": "that \u03c9p\u03bb ( x, \u222b t 0 \u0398 (m\u22121)/m 2 (s)ds ) \u03c9\u03bb ( x, \u222b t 0 \u0398 (m\u22121)/m 1 (s)ds ) = ( 1 + \u222b t 0 \u0398 (m\u22121)/m 2 (s)ds )\u2212p\u00b5( 1 + \u222b t 0 \u0398 (m\u22121)/m 1 (s)ds )\u00b5 \u00d7 ( 1 + (1\u2212m)\u00b5 (2\u2212 \u03bb)m ( 1 + \u222b t 0 \u0398 (m\u22121)/m 2 (s)ds )\u2212(2\u2212\u03bb)\u00b5 x2\u2212\u03bb )(p\u22121)/(m\u22121) \u00d7 (1 + (1\u2212m)\u00b5 (2\u2212\u03bb)m ( 1 + \u222b t 0 \u0398 (m\u22121)/m 2 (s)ds )\u2212(2\u2212\u03bb)\u00b5 x2\u2212\u03bb 1 + (1\u2212m)\u00b5 (2\u2212\u03bb)m ( 1 + \u222b t 0 \u0398 (m\u22121)/m 1 (s)ds )\u2212(2\u2212\u03bb)\u00b5 x2\u2212\u03bb )1/(m\u22121) \u2264 ( 1 + \u222b t 0 \u0398 (m\u22121)/m 2 (s)ds )\u2212p\u00b5( 1 + \u222b t 0 \u0398 (m\u22121)/m 1 (s)ds )\u00b5 , x \u2265 0, t \u2265 0, 14 X. ZHAO, M. ZHOU, Q. ZHOU EJDE-2022/73 and similarly, \u03c9q\u03bb ( x, \u222b t 0 \u0398 (m\u22121)/m 1 (s)ds ) \u03c9\u03bb ( x, \u222b t 0 \u0398 (m\u22121)/m 2 (s)ds ) \u2264 ( 1 + \u222b t 0 \u0398 (m\u22121)/m 1 (s)ds )\u2212(q\u22121)\u00b5+1/(1\u2212m)( 1 + \u222b t 0 \u0398 (m\u22121)/m 2 (s)ds )1/(m\u22121) for x \u2265 0 and t \u2265 0. = \u0398 1/m 1 (t)\u03c9\u03bb ( x, \u222b t 0 \u0398 (m\u22121)/m 1 (s)ds ) , x \u2265 0, t \u2265 0, (4.23) v\u0302(x, t)", "mime": "application/pdf"}, {"id": "ejde-1633", "words": "7508", "extension": ".pdf", "flesch": "79", "author": "Wu, Xinrui; Liang, Xingyu", "title": "Global well-posedness of 3D inhomogeneous incompressible nematic liquid crystal\u00a0systems in critical Besov spaces with initial density perturbed around the equilibrium", "date": "2025", "keywords": "b\u0307 \u22121; estimate; global; liquid; lp(r3; l\u221e(0,t; p p,1; spaces; system; \u22121 +", "summary": "Their result require 0 < c0 \u2264 \u03c10 \u2264 C0 < +\u221e and small norm \u2225(u0,\u2207d0)\u2225B\u03071/2 2,1 (R3) . \u2264 C\u2225\u2207d\u2225Ls,1(0,T ;Lm(R3))\u2225t\u22072d\u2225L\u221e(0,T ;L\u221e(R3)) \u2264 C\u2225\u2207d\u2225Ls,1(0,T ;Lm(R3))\u2225t\u2207d\u2225 L\u221e(0,T ;B\u0307 1+ 3 m m,1 (R3)) .", "mime": "application/pdf"}, {"id": "ejde-1648", "words": "14427", "extension": ".pdf", "flesch": "74", "author": "Unlu, Mehmet", "title": "Inverse scattering method for an integrable system of derivative nonlinear Schrodinger equations", "date": "2025", "keywords": "matrix; scattering; solutions; system", "summary": "= K1(x, x)K\u03042(x, x). \u2212 rxx \u2212 iqrrx = 0, (1.1) where x and t are the independent variables taking values on the real axis R, the subscripts denote the respective partial derivatives, the dependent variables q and r are complex-valued functions of x and t.", "mime": "application/pdf"}, {"id": "ejde-1658", "words": "15320", "extension": ".pdf", "flesch": "83", "author": "Karakostas, George L.", "title": "Existence of solutions for a n-dimensional systems of nonlocal boundary value problems", "date": "2025", "keywords": "+ a\u22121; a0 \u222b; a1 \u222b; b1\u03b8(1)\u22121 \u222b; ds\u2212b1\u03b8(1)\u22121 \u222b; nx)(u; nx)(u)du; value; \u03b8(s)\u22121 \u222b; \u03c80[x; \u03c81[x; \u2212 \u222b; \u222b t", "summary": "+ \u222b t 0 \u0398(s)\u22121ds\u0398(0)x\u2032(0) + \u222b t 0 \u0398(s)\u22121 \u222b s 0 (Nx)(u) du ds, (2.4) which will be used to express the solution as a fixed point of an operator equation. The quantity \u03c11 := V (A\u22121 0 \u03a80) + \u2225(A\u22121 0 B0 + \u222b 1 0 \u0398(s)\u22121ds\u0398(0))P\u22121 1 \u2225E ( V (A0\u03a81) + V (A1\u03a80) ) satisfies the condition \u03c11 < 1 and moreover condition (H0) is satisfied with \u03c11 and the constants M1 := \u2225(A\u22121 0 B0 + \u222b t 0 \u0398(s)\u22121ds\u0398(0))P\u22121( \u222b 1 u \u0398(s)\u22121ds+B1\u0398(1)\u22121)\u2225E + \u222b 1 0 \u2225\u0398(s)\u22121\u2225Eds, K1 := |A\u22121 0", "mime": "application/pdf"}, {"id": "ejde-166", "words": "4925", "extension": ".pdf", "flesch": "74", "author": "Barbatis, Gerassimos; Branikas, Panagiotis", "title": "Heat kernel estimates for fourth-order non-uniformly elliptic operators with non-strongly convex symbols", "date": "2022", "keywords": "q(x", "summary": "This implies [1, Theorem 7.12] an analogous inequality for the symbol A(x, \u03be) of H, namely ReA(x, \u03be) \u2265 cw(x)|\u03be|4 , x \u2208 \u2126 , \u03be \u2208 R2. We define the weighted Sobolev space W 1,\u221e w (\u2126) = {u \u2208W 1,\u221e loc (\u2126) : \u2203c \u2265 0 : |u(x)| \u2264 cw(x), |\u2207u(x)| \u2264 cw(x)3/4, x \u2208 \u2126}.", "mime": "application/pdf"}, {"id": "ejde-1668", "words": "10636", "extension": ".pdf", "flesch": "62", "author": "Zheng, Jiashan; Wang, Yuying", "title": "Blow-up prevention and rate of convergence of solutions for N-dimensional parabolic-parabolic systems with consumption of chemoattractant", "date": "2025", "keywords": "chemotaxis; lemma; system", "summary": "+ \u222b t 0 \u2225\u2207e(t\u2212s)\u2206u(\u00b7, s)v(\u00b7, s)\u2225Lq(\u2126)ds \u2264 C1 + C2 \u222b t 0 ( 1 + (t\u2212 s)\u2212 1 2\u2212 N 2 ( 1 k\u2212 1 q ) ) e\u2212\u03bb1(t\u2212s)\u2225u(\u00b7, s)v(\u00b7, s)\u2225Lk(\u2126) (4.22) for all t \u2208 (0, Tmax), where \u03bb1 is the first positive eigenvalue of \u2212\u2206 under homogeneous Neumann boundary conditions. From (4.21)and the identity \u22121 2 \u2212 N 2 (1 k \u2212 1 q ) > \u22121 (4.23) we obtain \u222b t 0 ( 1 + (t\u2212 s)\u2212 1 2\u2212 N 2 ( 1 k\u2212 1 q ) ) e\u2212\u03bb1(t\u2212s)ds \u2264 \u222b \u221e 0 ( 1 + \u03c3\u2212 1 2\u2212 N 2 ( 1 k\u2212 1 q ) ) e\u2212\u03bb1\u03c3d\u03c3 < +\u221e for all t \u2208 (0, Tmax), (4.24) and that for some C3 > 0, the latter on the right-hand side of (4.22) bringing together (4.23)-(4.24) also trivially provides C2 \u222b t 0 ( 1 + (t\u2212 s)\u2212 1 2\u2212 N 2 ( 1 k\u2212 1 q ) )", "mime": "application/pdf"}, {"id": "ejde-167", "words": "6618", "extension": ".pdf", "flesch": "83", "author": "Kratou, Mouna", "title": "Kirchhoff systems involving fractional p-Laplacian and singular nonlinearity", "date": "2022", "keywords": "p\u2212q", "summary": "\u03b2 < 1, 2\u2212 \u03b1\u2212 \u03b2 < p \u2264 p\u03b8 < q < p\u2217s, then, there exists a number \u039b0 = (q + \u03b1+ \u03b2 \u2212 2 \u2016c\u2016\u221ek(q \u2212 p) ) p p+\u03b1+\u03b2\u22122 ( 2\u2212 \u03b1\u2212 \u03b2 \u2212 q k(2\u2212 \u03b1\u2212 \u03b2 \u2212 p) |\u2126| p\u2217s\u2212q p\u2217s )\u2212 p p\u2212q S 2\u2212\u03b1\u2212\u03b2 p+\u03b1+\u03b2\u22122 , such that for 0 < (\u03bb\u2016a\u2016\u221e) p p\u2212q + (\u00b5\u2016b\u2016\u221e) p p\u2212q < \u039b0, problem (1.1) has at least two nontrivial positive solutions. There exists \u039b0 = (q + \u03b1+ \u03b2 \u2212 2 \u2016c\u2016\u221ek(q \u2212 p) ) p p+\u03b1+\u03b2\u22122 ( 2\u2212 \u03b1\u2212 \u03b2 \u2212 q k(2\u2212 \u03b1\u2212 \u03b2 \u2212 p) |\u2126| 2\u2217s\u2212q 2\u2217s )", "mime": "application/pdf"}, {"id": "ejde-168", "words": "5505", "extension": ".pdf", "flesch": "76", "author": "Dutta, Prerona", "title": "Extending Lagrangian transformations to nonconvex scalar conservation laws", "date": "2022", "keywords": "conservation; system", "summary": "\ufffd In conclusion, we observe that \u03c1 is an admissible weak solution to the Cauchy problem for the scalar conservation law (2.4) where \u03c1 = \u03c3 \u2212 L and \u03c3 is given by (2.20). Finally we establish that entropy admissible weak solutions to this system are equivalent to those of the scalar equation.", "mime": "application/pdf"}, {"id": "ejde-1684", "words": "9096", "extension": ".pdf", "flesch": "79", "author": "Liu, Qingbo; Zhao, Lan", "title": "Global bifurcation for semilinear eigenvalue problems involving nonlocal terms", "date": "2025", "keywords": "eigenvalue; theorem", "summary": "In this situation, \u03c8\u2032(|\u03b1|2/2) = \u03bb1 \u2212 \u03bb1 = 0. Case 2: \u03bb = \u03bb1.", "mime": "application/pdf"}, {"id": "ejde-169", "words": "13968", "extension": ".pdf", "flesch": "89", "author": "Correia, Jeziel N.; Oliveira, Claudionei P.", "title": "Existence of positive solutions for fractional Laplacian systems with critical growth", "date": "2022", "keywords": "ds,2(rn; lemma; on(1; y|n+2s; |x\u2212", "summary": "\u00d7 Lqloc(RN ), (un, vn)\u2192 (u, v) a.e. in RN \u00d7 RN . Arguing in the same way, we have\u222b RN b(x)|\u03a6\u03b4,b|2dx \u2264 |b|q|\u03a6\u03b4,0|22t, \u2200b \u2208 RN . From Lemma 4.1(iii), given \u03b5 > 0 there exists \u03b4 = \u03b4(\u03b5) > 0 such that sup b\u2208RN f(`0\u03a6\u03b4,b, t0\u03a6\u03b4,b) \u2264 SH + \u03b5 2 + \u03b5 2 \u2264 SH + \u03b5, \u2200\u03b4 \u2208 (0, \u03b4].", "mime": "application/pdf"}, {"id": "ejde-17", "words": "8739", "extension": ".pdf", "flesch": "78", "author": "Anh, Nguyen Thi Van; Yen, Bui Thi Hai", "title": "Existence and controllability for neutral partial differential inclusions nondenselly defined on a half-line", "date": "2023", "keywords": "d(a; differential; lim; s\u2032(t\u2212; \u2016p\u2016", "summary": "Pyt + lim\u03bb\u2192\u221e \u222b t 0 S\u2032(t\u2212 s)R\u03bbLysds + lim\u03bb\u2192\u221e \u222b t 0 S\u2032(t\u2212 s)R\u03bbg(s)ds, g \u2208 SF,y, if t \u2208 J. It is clear that the fixed points of the operator N are integral solutions of the problem (1.1)-(1.2). To be precise, the following equation was considered on the whole line d dt D(xt) = AD(xt) + L(xt) + f(t), t \u2208 R. The authors proved the existence of an almost automorphic solution for above equation and applied abstract results to a neutral wave equation with delay.", "mime": "application/pdf"}, {"id": "ejde-171", "words": "13378", "extension": ".pdf", "flesch": "77", "author": "Baroni, Paolo; Coscia, Alessandra", "title": "Gradient regularity for non-autonomous functionals with Dini or non-Dini continuous coefficients", "date": "2022", "keywords": "b2r; estimate; lemma; regularity; \u2212 \u222b; \u2223\u22232", "summary": "In particular, when p \u2265 2, |z1 \u2212 z2|p \u2264 c|Vp(z1)\u2212 Vp(z2)|2 holds, while for 1 < p \u2264 2 (see [38, Lemma 2]) we will use that |z1 \u2212 z2| \u2264 c \u2223\u2223Vp(z1)\u2212 Vp(z2) \u2223\u22232/p + c|z1|(2\u2212p)/2 \u2223\u2223Vp(z1)\u2212 Vp(z2) \u2223\u2223 (2.24) EJDE-2022/80 REGULARITY FOR DOUBLE PHASE FUNCTIONALS 9 both for a suitable constant c \u2261 c(p). |z2|)|z1 \u2212 z2|2 \u2264 \u2223\u2223V\u03d5(z1)\u2212 V\u03d5(z2) \u2223\u22232 \u2264 c\u03d5\u2032\u2032(|z1|+", "mime": "application/pdf"}, {"id": "ejde-1712", "words": "9203", "extension": ".pdf", "flesch": "75", "author": "Dias, Fabio Scalco; Oliveira, Regilene; Valls, Claudia", "title": "Dynamics of a May-Leonard asymmetric system of ordinary differential equations", "date": "2025", "keywords": "s s; sn s; system; un s", "summary": "Regions r0 r1 r2 r3 s0 s1 w0 PP R1 UN SN S S UN SN S R1 R2 UN S S SN UN S UN R1 R3 UN S S S UN SN UN R3 R4 UN S SN S S UN UN R1 R5 UN S SN SN S S UN R5 R6 UN SN SN S S UN S R5 R7 UN SN S SN UN S S R5 L1,2 UN S-N S r1 UN \u2204 S-N L1,2 L2,3 UN S S \u2204 UN S-N UN L2,3 L2,4 UN S S-N r2 S-N s0 UN L1,2 L4,5 UN S SN \u2204 p0 p1 p2 p3 q1 q2 w0 PP R1 S SN UN S S SN UN R1 R2 S S UN SN UN S UN R2 R3 S SN UN S UN S UN R3 R4 S SN UN S S UN UN R1 R5 UN SN S S S UN UN R3 R6 UN S S SN S UN UN R1 R7 S UN SN S S UN UN R1 R8 S UN SN S UN S UN R3 R9 UN S S SN UN S UN R3 R10 UN SN S S UN S UN R3 R11 S S SN UN UN S UN R2 R12 S UN SN S S SN UN R1 R13 UN S S SN S SN UN R1 R14 UN SN S S S SN UN R3 P1 S-N \u2204", "mime": "application/pdf"}, {"id": "ejde-172", "words": "6975", "extension": ".pdf", "flesch": "79", "author": "Lin, Xiaolu; Zheng, Shenzhou", "title": "Mixed local and nonlocal Schrodinger-Poisson type system involving variable exponents", "date": "2022", "keywords": "lemma; schro\u0308dinger; solutions; theorem", "summary": "= \u03b1|u|p(x)\u22122u+ \u03b2|u|q(x)\u22122u in \u2126, \u2212\u2206\u03c6 = up in \u2126, u = \u03c6 = 0 in RN \\ \u2126, (1.1) where \u03bb is a positive parameter, and V (x) \u2208 C(RN ) is a potential function. = u(x)e\u2212\u0131t to the time-dependent Schro\u0308dinger-Poisson system \u2212i\u2202\u03c8 \u2202t = \u2212\u2206\u03c8 + \u03c6(x)\u03c8 \u2212 f(\u03c8) in \u2126, \u2212\u2206\u03c6 = |\u03c8|2 in \u2126, \u03c8 = \u03c6 = 0 on \u2202\u2126. (1.2)", "mime": "application/pdf"}, {"id": "ejde-174", "words": "6763", "extension": ".pdf", "flesch": "87", "author": "Zhao, Haiqin; Wu, Shi-Liang", "title": "Regular traveling waves for a reaction-diffusion equation with two nonlocal delays", "date": "2022", "keywords": "waves", "summary": "f(U2(\u03be1 \u2212 y \u2212 c\u03c41))]dy + \u03c92 \u222b R \u03932(D2\u03c42, y)[f(U1(\u03be1 \u2212 y \u2212 c\u03c42))\u2212 f(U2(\u03be1 \u2212 y \u2212 c\u03c42))]dy \u2264 \u2212\u00b5\u03a0(\u03be1)e\u03bd1\u03be1 + \u03c91f \u2032(0) \u222b R \u03931(D1\u03c41, y) \u00d7max{0, U1(\u03be1 \u2212 y \u2212 c\u03c41)\u2212 U2(\u03be1 \u2212 y \u2212 c\u03c41)}dy + \u03c92f \u2032(0) \u222b R \u03932(D2\u03c42, y) max{0, U1(\u03be1 \u2212 y \u2212 c\u03c41))dy + \u03c91 \u222b R \u03932(D2\u03c42, y)f(U(\u03be \u2212 y \u2212 c\u03c42))dy = 0, (2.2) where \u03c91 := pe\u2212d1\u03c41 and \u03c92 := (1\u2212 p)e\u2212d2\u03c42 .", "mime": "application/pdf"}, {"id": "ejde-175", "words": "4352", "extension": ".pdf", "flesch": "79", "author": "Han, Xiao; He, Yujing; Wei, Hui", "title": "Existence of positive periodic solutions for a nonlinear system of second-order ordinary differential equations", "date": "2022", "keywords": "solutions", "summary": "By using the fixed point theorem of cone expansion and compression we obtain the existence of positive periodic solutions. Existence ofsolutions; positive periodic solutions; fixed point theorem.", "mime": "application/pdf"}, {"id": "ejde-176", "words": "11920", "extension": ".pdf", "flesch": "77", "author": "Ortegon Gallego, Francisco; Ouyahya, Hakima; Rhoudaf, Mohamed", "title": "Existence of a solution and its numerical approximation for a strongly nonlinear coupled system in anisotropic Orlicz-Sobolev spaces", "date": "2022", "keywords": "ai(x; d\u2211 i=1; i=1; solution; \u03c9 ai(x", "summary": "It consists of two coupled nonlinear elliptic equations governing the temperature, u, and the electric potential, \u03d5, inside a semiconductor device, namely, \u2212A(u) = \u03c1(u)|\u2207\u03d5|2 in \u2126 div(\u03c1(u)\u2207\u03d5) = 0 in \u2126, \u03d5 = \u03d50 on \u2202\u2126, u = 0 on \u2202\u2126, (1.1) where \u2126 \u2282 Rd (the thermistor geometry) is a bounded domain, d \u2265 2 is an integer, and the operator A, given by A(u) , d, the function ai(x, s, \u03b6) : \u2126\u00d7R\u00d7R 7\u2192 R is a Carathe\u0301odory function, that is, measurable with respect to x in \u2126 for all (s, \u03b6) \u2208 R2, and continuous with respect to (s, \u03b6) for", "mime": "application/pdf"}, {"id": "ejde-177", "words": "8698", "extension": ".pdf", "flesch": "76", "author": "Molica Bisci, Giovanni; Servadei, Raffaella; Zhang, Binlin", "title": "Monotonicity properties of the eigenvalues of nonlocal fractional operators and their applications", "date": "2022", "keywords": "a.e; f(x; problem; theorem", "summary": "The space Xs 0(\u2126) is defined as Xs 0(\u2126) := { g \u2208 X : g = 0 a.e. in Rn \\ \u2126 } , EJDE-2022/85 MONOTONICITY PROPERTIES OF EIGENVALUES 5 where X denotes the linear space of Lebesgue measurable functions from Rn to R such that the restriction to \u2126 of any function g in X belongs to L2(\u2126) and the map (x, y) 7\u2192 (g(x)\u2212 g(y)) \u2223\u2223 6 q\u03bd(x) a.e. x \u2208 Rn (4.43) for all j \u2208 N. By (1.5), (4.42), (4.43), and the Lebesgue Dominated Convergence Theorem, we obtain that \u222b \u2126 f(x, uj(x))uj(x)dx\u2192 \u222b \u2126 f(x, u\u221e(x))u\u221e(x) dx\u222b \u2126 f(x, uj(x))u\u221e(x) dx\u2192 \u222b \u2126 f(x, u\u221e(x))u\u221e(x) dx (4.44) as j \u2192 +\u221e, while, by (1.7) and (4.42) we obtain\u222b \u2126 g(x)uj(x) dx\u2192 \u222b \u2126 g(x)u\u221e(x) dx (4.45) as j \u2192 +\u221e.", "mime": "application/pdf"}, {"id": "ejde-178", "words": "11245", "extension": ".pdf", "flesch": "82", "author": "Xu, Jiaohui; Caraballo, Tomas", "title": "Well-posedness of stochastic time fractional 2D-Stokes models with finite and infinite delay", "date": "2022", "keywords": "2\u03b1\u2212; f t; fractional; lemma; sup; time", "summary": "+ \u222b t 0 (t\u2212 s)\u03b1\u22121E\u03b1,\u03b1(\u2212(t\u2212 s)\u03b1A)F (s, us)ds + \u222b t 0 (t\u2212 s)\u03b1\u22121E\u03b1,\u03b1(\u2212(t\u2212 s)\u03b1A)G(s, us)dW (s), t \u2208 (0, T ], P-a.s. (3.5) On the other hand, for t \u2208 (0, T ], we have E\u2016(Nu)(t)\u20162 \u2264 3E\u2016E\u03b1(\u2212t\u03b1A)\u03d5(0)\u20162 + 3E \u2225\u2225 \u222b t 0 (t\u2212 s)\u03b1\u22121E\u03b1,\u03b1(\u2212(t\u2212 s)\u03b1A)F (s, us)ds \u2225\u22252 + 3E \u2225\u2225 \u222b t 0 (t\u2212 s)\u03b1\u22121E\u03b1,\u03b1(\u2212(t\u2212 s)\u03b1A)G(s, us)dW (s) \u2225\u22252 := I1 + I2 + I3. (3.6) Now we estimate each term on the right-hand side of (3.6).", "mime": "application/pdf"}, {"id": "ejde-179", "words": "9200", "extension": ".pdf", "flesch": "78", "author": "Camasta, Alessandro; Fragnelli, Genni", "title": "Fourth-order differential operators with interior degeneracy and generalized Wentzell boundary conditions", "date": "2022", "keywords": "a(0; boundary; conditions; h2 a(0", "summary": "Thus, we introduce Y := { u \u2208 H2 1/a(0, 1) : u(x0) = (au\u2032)(x0) = 0 } and, proceeding as in [9] and [21] (if x0 \u2208 {0, 1}) or as in [7] (if x0 \u2208 (0, 1)), one can prove the following result. If u0 \u2208 X\u00b5 and h \u2208 L2(0, T ;X\u00b5), a function u is said to be a weak solution of (3.7) if u \u2208 C ( [0, T ];X\u00b5 ) \u2229 L2 ( 0, T ;H2 a(0, 1) ) and\u222b 1 0 u(T, x)\u03d5(T, x) dx\u2212 \u222b 1 0 u0(x)\u03d5(0, x) dx\u2212 \u222b (0,T )\u00d7(0,1) u(t, x)\u03d5t(t, x) dx dt + a(1)u(T, 1)\u03d5(T, 1) \u03b21 \u2212 a(1)u0(1)\u03d5(0, 1) \u03b21 \u2212 a(1) \u03b21 \u222b T 0 u(t, 1)\u03d5t(t, 1)dt + a(0)u(T, 0)\u03d5(T, 0) \u03b20 \u2212 a(0)u0(0)\u03d5(0, 0) \u03b20 \u2212 a(0) \u03b20 \u222b T 0 u(t, 0)\u03d5t(t, 0)dt = \u2212 \u222b (0,T )\u00d7(0,1) a(x)uxx(t, x)\u03d5xx(t, x) dx dt\u2212 \u03b31 \u03b21 \u222b T 0 a(1)u(t, 1)\u03d5(t, 1)dt \u2212 \u03b30 \u03b20 \u222b T 0 a(0)u(t, 0)\u03d5(t, 0)dt+ \u222b (0,T )\u00d7(0,1) h(t, x)\u03d5(t, x) dx dt + \u222b T 0 a(1)h(t, 1)\u03d5(t, 1)", "mime": "application/pdf"}, {"id": "ejde-1792", "words": "5138", "extension": ".pdf", "flesch": "73", "author": "Munoz Rivera, Jaime; Ochoa Ochoa, Elena; Quintanilla, Ramon ", "title": "Thermoelastic plates with type I heat conduction with second gradient", "date": "2025", "keywords": "equation; semigroup; solutions", "summary": "d i\u03c9 \u222b \u2126 \u2206\u03b8(i\u03c1\u03c9v \u2212 \u03b7\u2206\u03b8 \u2212 g2)d\u2126 = d\u03c1 \u222b \u2126 \u2206\u03b8 v d\u2126+ d i\u03c9 \u222b \u2126 \u03b7|\u2206\u03b8|2d\u2126+ d i\u03c9 \u222b \u2126 \u2206\u03b8g2d\u2126. Finally, multiplying equation (2.6) by u we find that i\u03c1 \u222b \u2126 \u03c9vu d\u2126+ c \u222b \u2126 |\u2206u|2 d\u2126\u2212 \u03b7 \u222b \u2126 \u2206\u03b8u d\u2126 = \u222b \u2126 g2u d\u2126. Using equation (2.5) we obtain \u03c1 \u222b \u2126 |v|2 d\u2126 = \u2212\u03c1 \u222b \u2126 vg1 d\u2126+ c \u222b \u2126 |\u2206u|2 d\u2126\u2212 \u03b7 \u222b \u2126 \u2206\u03b8u d\u2126\u2212 \u222b \u2126 g2u d\u2126. The above inequality implies\u222b \u2126 |v|2 d\u2126 \u2264 c \u222b \u2126 |\u2206u|2 d\u2126+ c \u222b \u2126 |\u2206\u03b8|2 d\u2126+ c\u0303\u03f5\u2225U\u2225H\u2225G\u2225H. Using (3.3) and (2.8) we obtain\u222b \u2126 |v|2 d\u2126 \u2264 c\u0303\u03f5\u2225U\u2225H\u2225G\u2225H + c\u0303\u2225G\u22252H, for \u03f5 small.", "mime": "application/pdf"}, {"id": "ejde-1794", "words": "5491", "extension": ".pdf", "flesch": "74", "author": "Almeida, Wendy F.; Figueiredo, Giovany M.", "title": "Solutions to magnetic Schrodinger equations with arbitrary growth at infinity", "date": "2025", "keywords": "g(x; magnetic", "summary": "Recently, the study of magnetic Schro\u0308dinger equations has been approached from various per- spectives, however only a limited number of works have addressed this topic. Magnetic Schro\u0308dinger equations; arbitrary growth at infinity.", "mime": "application/pdf"}, {"id": "ejde-180", "words": "7278", "extension": ".pdf", "flesch": "82", "author": "Xie, Zheng; Chen, Jing", "title": "Multiplicity of solutions for a generalized Kadomtsev-Petviashvili equation with potential in R^2", "date": "2023", "keywords": "problem; solutions", "summary": "\u2022 for x \u2208 R2 and r > 0, Br(x) := {y \u2208 R2 : |y \u2212 x| < r}. In view of (A4), (A5), (A7), and (A10), it is easy to deduce that g is a Carathe\u0301odory function and satisfying the following properties: (A11) g(x, y, t) \u2264 \u03b4t+ f(t) for any t \u2265 0 and \u03b4 \u2265 0; (A12) limt\u21920 g(x,y,t) t = 0 uniformly in (x, y) \u2208 R2; (A13) 0 < 2G(x, y, t)", "mime": "application/pdf"}, {"id": "ejde-181", "words": "7192", "extension": ".pdf", "flesch": "78", "author": "Duan, Yubo; Jiang, Yiming; Tian, Yang; Wei, Yawei", "title": "Stochastic Burgers equations with fractional derivative driven by fractional noise", "date": "2023", "keywords": "c(\u03b1; \u222b \u221e", "summary": "L\u03b1\u03b2,\u03b2(t2 \u2212 s)B(u(s))ds\u2016p H\u0307\u03b3 = E\u2016 \u222b t1 0 ( (t2 \u2212 s)\u03b2\u22121 \u2212 (t1 \u2212 s)\u03b2\u22121 ) A\u03b3L \u03b1 \u03b2,\u03b2(t2 \u2212 s)B(u(s))ds\u2016p 6 C(\u03b1, \u03b2, \u03b3)E (\u222b t1 0 \u2016((t2 \u2212 s)\u03b2\u22121 \u2212 (t1 \u2212 s)\u03b2\u22121)(t2 \u2212 s)\u2212 \u03b2\u03b3 \u03b1 \u2016\u2016B(u(s))\u2016ds )p 6 C(\u03b1, \u03b2, \u03b3,M, p) (\u222b t1 0 ( (t1 \u2212 s)\u03b2\u22121 \u2212 (t2 \u2212 s)\u03b2\u22121 ) p p\u22121 (t2 \u2212 s)\u2212 p\u03b2\u03b3 \u03b1(p\u22121) ds ) B(u(s))ds\u2016p 6 E (\u222b t1 0 (t1 \u2212 s)\u03b2\u22121\u2016A\u03b3 ( L\u03b1\u03b2,\u03b2(t2 \u2212 s)\u2212 L\u03b1\u03b2,\u03b2(t1 \u2212 s) ) B(u(s))\u2016ds )p 6 C(\u03b1, \u03b2, \u03b3)(t2 \u2212 t1) p\u03b2\u03b3 \u03b1 E (\u222b t1 0 (t1 \u2212 s)\u03b2\u22121\u2016B(u(s))\u2016ds )p .", "mime": "application/pdf"}, {"id": "ejde-1812", "words": "7228", "extension": ".pdf", "flesch": "78", "author": "Liang, Jin; Mu, Yunyi; Xiao, Ti-Jun", "title": "Evolution psi-Hilfer fractional differential equations in Banach spaces", "date": "2025", "keywords": "differential; equations; fractional", "summary": "respectively:( D\u03b1,\u03b2;\u03c8x ) (t) = Ax(t) + f ( t, x(t), \u222b t 0 \u03c1(t, s)x(s)ds ) , 0 < \u03b1 < 1, 0 \u2264 \u03b2 \u2264 1, t \u2208 (0, b], I1\u2212\u03b3;\u03c8x(0) = x0, \u03b1 \u2264 \u03b3 = \u03b1+ \u03b2 \u2212 \u03b1\u03b2 < 1, (4.4) and( D\u03b1\u2032,\u03b2\u2032;\u03c8y ) (t) = Ay(t) + f ( t, y(t), \u222b t 0 \u03c1(t, s)y(s)ds ) , 0 < \u03b1\u2032 < 1, 0 \u2264 \u03b2\u2032 As a matter of fact, for each x1, x2 \u2208 C1\u2212\u03b1\u2212\u03b2(1\u2212\u03b1);\u03c8(J,X) and t \u2208 J , we can obtain \u03c81\u2212\u03b1\u2212\u03b2(1\u2212\u03b1)(t)\u2225(Tx1)(t)\u2212 (Tx2)(t)\u2225 \u2264 \u03c81\u2212\u03b1\u2212\u03b2(1\u2212\u03b1)(t) \u222b t 0 \u2225K\u03b1(\u03c8(t)\u2212 \u03c8(s))[f(s, x1(s))\u2212 f(s, x2(s))]\u2225\u03c8\u2032(s)ds \u2264 M\u21132 \u0393(\u03b1) \u03c81\u2212\u03b1\u2212\u03b2(1\u2212\u03b1)(t) \u222b t 0 (\u03c8(t)\u2212 \u03c8(s))\u03b1\u22121\u03c8\u03b1+\u03b2(1\u2212\u03b1)\u22121(s) 6 J. LIANG, Y. MU, T.-J. XIAO EJDE-2025/109 \u00d7 \u03c81\u2212\u03b1\u2212\u03b2(1\u2212\u03b1)(s)\u2225x1(s)\u2212 x2(s)\u2225\u03c8\u2032(s)ds \u2264 \u0393(\u03b1+ \u03b2(1\u2212 \u03b1))M\u21132\u03c8 \u03b1(t) \u0393(2\u03b1+ \u03b2(1\u2212 \u03b1)) \u2225x1", "mime": "application/pdf"}, {"id": "ejde-1820", "words": "9484", "extension": ".pdf", "flesch": "66", "author": "Mishra, Shivam Kumar; Abbas, Syed; Nieto, Juan Jose", "title": "Periodic solution and stationary distribution of a stochastic epidemic modelwith two different epidemics and different epidemiological frameworks", "date": "2025", "keywords": "epidemic; model; stochastic; system", "summary": "\u2212 lnI1 \u2212 lnI2 + \u03ba(t). Therefore, in recent times, many studies have been done on stochastic epidemic models and researchers have demonstrated how environmental noise affects population model dynamics (see [11, 22, 7]).", "mime": "application/pdf"}, {"id": "ejde-183", "words": "3894", "extension": ".pdf", "flesch": "83", "author": "Abebe, Abraham; Chhetri, Maya", "title": "A nonexistence result for p-Laplacian systems in a ball", "date": "2023", "keywords": "p\u22121", "summary": "See also [10], where nonexistence of positive solutions is established when a weight function is large for a semipositone superlinearproblem in a ball. In this case, however, the nonexistence result for positive solution for \u03bb large has been extended to the case when \u2126 is a smooth bounded domain in RN (N \u2265 2) in [4].", "mime": "application/pdf"}, {"id": "ejde-184", "words": "11944", "extension": ".pdf", "flesch": "82", "author": "Bao, Qinglan; Wei, Guangsheng; Zettl, Anton", "title": "Friedrichs extension of singular symmetric differential operators", "date": "2023", "keywords": "differential; friedrichs; matrix; operator; solution; theorem", "summary": "C\u22121 = \u2212C = C\u2217, (1.1) and let Z2n(I) := {(qr,s)2nr,s=1 \u2208M2n(L1 loc(I)), qr,r+1 6= 0 We have G\u0302 = ( 0 G1 \u2212G\u22171 0 ) , G1 = ( C\u0302da\u2212n 0 0 \u2212C\u0302db\u2212n ) .", "mime": "application/pdf"}, {"id": "ejde-185", "words": "12051", "extension": ".pdf", "flesch": "78", "author": "Behncke, Horst; Hinton, Don", "title": "Spectral theory of C-symmetric non-selfadjoint differential operators of order 2n", "date": "2023", "keywords": "case; coefficients; conditions; differential; exp; operators; selfadjoint; spectrum; theorem", "summary": "Since the Fredholm index of Tmin \u2212 z is constant in K0 and dimN(Tmax\u2212 z) = dimN(T+ max\u2212 z\u0304), it follows that (H1) holds in K0. = { \u03a6\u0303(x, z)\u03c7\u2217(t, z), a \u2264 x \u2264 t, \u03c7(x, z)\u03a6\u2217(t, z), a \u2264 t < x, (3.10) are the integral kernels or Green\u2019s functions of the resolvents Rz = (T\u03b1 \u2212 z)\u22121, respectively R\u0303z = (T+ \u03b1 \u2212 z), i.e., (Rzf)(x) = \u222b \u221e a G(z, x, t)A(t)F (t)dt. where F is as in (4.5) below.", "mime": "application/pdf"}, {"id": "ejde-1857", "words": "13892", "extension": ".pdf", "flesch": "83", "author": "Boussetouan, Imane; Amrouche, Cherif", "title": "Existence and regularity of solutions for elliptic systems with mixed boundary conditions", "date": "2025", "keywords": "problem; solution", "summary": "(iii) Furthermore, if \u2126 is of class C 2,1, f \u2208 Lp(\u2126), a\u00d7 n \u2208 W2\u22121/p,p(\u0393N ), g \u2208W 1\u22121/p,p(\u0393N ), b \u2208W 2\u22121/p,p(\u0393D), and h\u00d7 n \u2208 W1\u22121/p,p(\u0393D), then u belongs to W2,p(\u2126) and \u2225u\u2225W2,p(\u2126) \u2264 C ( \u2225f\u2225Lp(\u2126) + \u2225g\u2225W 1\u22121/p,p(\u0393N ) + \u2225h\u00d7 n\u2225W1\u22121/p,p(\u0393D) + \u2225a\u00d7 n\u2225W2\u22121/p,p(\u0393N ) + \u2225b\u2225W 2\u22121/p,p(\u0393D) ) . Furthermore, if \u2126 is of class C 2,1, f \u2208 Lp(\u2126), g \u2208 W 1\u22121/p,p(\u0393N ), and h \u2208 W1\u22121/p,p(\u0393D) with F = 0, then u belongs to W2,p(\u2126) and \u2225u\u2225W2,p(\u2126) \u2264 C ( \u2225f\u2225Lp(\u2126) + \u2225g\u2225W 1\u22121/p,p(\u0393N ) + \u2225h\u2225W1\u22121/p,p(\u0393D) ) .", "mime": "application/pdf"}, {"id": "ejde-186", "words": "4092", "extension": ".pdf", "flesch": "65", "author": "Benedikt, Jiri; Pulpan, Jan", "title": "Numeric estimates of the principal eigenvalue of the p-Laplacian using interval arithmetic", "date": "2023", "keywords": "end; function; interval", "summary": "t = LinRange(0, 1, n-1) tI = [@interval(i) for i in t] U1 = [u[1] for u in sol(t).u] U1 I = [@interval(u[1]) for u in sol(t).u] U2 = [u[2] for u in sol(t).u] U2 I = [@interval(u[2]) for u in sol(t).u] return t, tI, U1, U1 I, U2, U2 I, \u039b1 end The function plaplace solve returns vectors U1 and U2 of numerical approxi- mations of the values of u1 = \u03d51,p and u2 at n (a parameter) equidistant division points t of the interval [0, 1]. Returns spline coefficients \u2018csc V\u2018 as well as interval values \u2018V\u2018 of the spline function.", "mime": "application/pdf"}, {"id": "ejde-188", "words": "6490", "extension": ".pdf", "flesch": "76", "author": "Castro, Alfonso; Jacobsen, Jon", "title": "Regular solutions to elliptic equations", "date": "2023", "keywords": "equations; solutions", "summary": "Nonlinear elliptic equation; radial solution; regular radial solution; singular radial solution; bifurcation analysis; Pohozaev identity; shooting method; superlinear nonlinearity; subcritical nonlinearity; sub-super critical nonlinearity; jumping nonlinearity. Similarly, when \u2126 is a ball or an annulus and g is radial in x, the existence of radial solutions to (1.2) is largely determined by the relation between g(x, u)/u and the set \u03c3rad(\u2212\u2206) = {\u03c1i : i = 1, 2, . . .}.", "mime": "application/pdf"}, {"id": "ejde-1891", "words": "9509", "extension": ".pdf", "flesch": "86", "author": "Wu , Jingpeng; Zhu, Min", "title": "Initial-boundary value problem of plasma-charge model in the half space", "date": "2025", "keywords": "plasma", "summary": "Then by (3.4) and take K2 large enough (depending only on K1,K) such that we have I\u0308 \u2265 h(Y (s),W (s))\u2212K1 \u2212 |Y \u2212 \u03be\u030a| ( |F\u03c1(Y )|+ \u03b4\u22122 0 ) \u2265 1 4 R2 \u2212K1 \u2212 C(l + 1)Q 4/3 t,\u03b4 \u2265 1 8 R2. Then by (3.4) and take K2 large enough (depending only on K1,K) such that we have I\u0308 \u2265 h(Y (s),W (s))\u2212K1 \u2212 |Y \u2212 \u03be\u030a| ( |F\u03c1(Y )|+ \u03b4\u22122 0 ) \u2265 1 16 Q2 t,\u03b4 \u2212K1 \u2212 C(l + 1)Q 4/3 t,\u03b4 \u2265 1 32 Q2 t,\u03b4.", "mime": "application/pdf"}, {"id": "ejde-19", "words": "15874", "extension": ".pdf", "flesch": "86", "author": "Levandosky, Julie L.; Vera, Octavio", "title": "Smoothing properties for a coupled Zakharov-Kuznetsov system", "date": "2023", "keywords": "c \u222b; case; solution; sup; term; |\u03b1| t; \u2202\u03b1uxxx; \u222b b; \u222b r2; \u222b t; \u222b \u03be\u03bd", "summary": "For \u03be\u03bd as defined in (6.3), \u03b1 = (\u03b11, \u03b12) such that |\u03b1| = \u03b2, 4 \u2264 \u03b2 \u2264 K, the following holds:\u2211 |\u03b1|=\u03b2 \u2223\u2223 \u222b t 0 \u222b \u03be\u03bd(\u2202\u03b1u)\u2202\u03b1(uux) \u2223\u2223+ \u2223\u2223 \u222b t 0 \u222b \u03be\u03bd(\u2202\u03b1v)\u2202\u03b1(vvx) \u2223\u2223 \u2264 C + C \u2211 |\u03b1|=\u03b2 (\u222b t 0 \u222b \u03be\u03bd(\u2202\u03b1u)2 ) + C \u2211 |\u03b1|=\u03b2 (\u222b t 0 \u222b \u03be\u03bd(\u2202\u03b1v)2 ) (6.21) for 0 \u2264 t \u2264 T , where C depends only on sup 0\u2264t\u2264T \u222b \u03be\u03bd(\u2202\u03b3u)2, sup 0\u2264t\u2264T \u222b \u03be\u03bd(\u2202\u03b3v)2, (6.22)\u222b T 0 \u222b (\u03be\u03bd)x(\u2202\u03b3ux)2, \u222b T 0 \u222b (\u03be\u03bd)x(\u2202\u03b3vx)2, (6.23)\u222b T 0 \u222b (\u03be\u03bd)x(\u2202\u03b3uy)2, \u222b T 0 \u222b (\u03be\u03bd)x(\u2202\u03b3vy)2 (6.24) for \u03b3 = (\u03b31, \u03b32) where |\u03b3| \u2264 \u03b2 \u2212 1. EJDE-2023/11 SMOOTHING PROPERTIES FOR ZAKHAROV-KUZNETSOV SYSTEMS 35 The proof uses the same ideas as in the proof of Lemma 3.2. In this case, the remainder terms satisfy\u2223\u2223 \u222b t 0 \u222b \u03beuxy(uux)xy \u2223\u2223 EJDE-2023/11 SMOOTHING PROPERTIES FOR ZAKHAROV-KUZNETSOV SYSTEMS 9 = \u2223\u2223 \u222b t 0 \u222b \u03beuxy(2uxuxy + uyuxx + uuxxy) \u2223\u2223 \u2264 |ux|L\u221e \u222b t 0 \u222b \u03beu2xy + C|uy|L\u221e \u222b t 0 \u222b \u03beu2xx + |uy|L\u221e \u222b t 0 \u222b \u03beu2xy \u2264 C \u222b t 0 \u222b \u03be(u2xx + u2xy) where C depends only on \u2016u\u2016H3 .", "mime": "application/pdf"}, {"id": "ejde-190", "words": "6745", "extension": ".pdf", "flesch": "76", "author": "Delgado, Briceyda B.; Pardo, Rosa", "title": "Resonant solutions for elliptic systems with Neumann boundary conditions", "date": "2023", "keywords": "1/\u00b5+; lim; solutions", "summary": "By the maximum principle [2, Theorem 4.1], for all h \u2265 0, h 6= 0, we have v = K h \u2208 P\u030a , where P\u030a = {u \u2208 C(\u2126): u > 0 in \u2126}. The nonlinearity f = (f1, f2), where fi : \u2126 \u00d7 R2 \u2192 R, i = 1, 2 are Carathe\u0301odory functions, that is, fi = fi ( x, s ) are measurable in x \u2208 \u2126 and continuous with respect to s = (s1, s2) \u2208 R2.", "mime": "application/pdf"}, {"id": "ejde-191", "words": "6745", "extension": ".pdf", "flesch": "76", "author": "Ghimenti, Marco G.; Micheletti, Anna Maria", "title": "Yamabe boundary problem with scalar-flat manifolds target", "date": "2023", "keywords": "1/\u00b5+; lim; solutions", "summary": "By the maximum principle [2, Theorem 4.1], for all h \u2265 0, h 6= 0, we have v = K h \u2208 P\u030a , where P\u030a = {u \u2208 C(\u2126): u > 0 in \u2126}. The nonlinearity f = (f1, f2), where fi : \u2126 \u00d7 R2 \u2192 R, i = 1, 2 are Carathe\u0301odory functions, that is, fi = fi ( x, s ) are measurable in x \u2208 \u2126 and continuous with respect to s = (s1, s2) \u2208 R2.", "mime": "application/pdf"}, {"id": "ejde-192", "words": "5805", "extension": ".pdf", "flesch": "71", "author": "Hollifield, Elliott", "title": "Positive solutions for nonlinear fractional Laplacian problems", "date": "2023", "keywords": "fractional; laplacian", "summary": "This charac- terization allowed them to prove several regularity results by using local techniques and provides a framework for interested researchers to further the study of the still emerging field of fractional Laplacian problems. [7] Maya Chhetri, Petr Girg; Some bifurcation results for fractional Laplacian problems.", "mime": "application/pdf"}, {"id": "ejde-195", "words": "4882", "extension": ".pdf", "flesch": "76", "author": "Knowles, Ian; Tamang, Sundar", "title": "Inverse volatility problem for currency options", "date": "2023", "keywords": "functional; volatility", "summary": "\u2212 wc,\u03bb)2. [ [(\u03bb+ rF )(w2 \u03bb \u2212 w2 c,\u03bb)\u2212 2\u03b2(w\u03bb \u2212 wc,\u03bb)] 2 K2\u03c12 + (w\u20322\u03bb \u2212 w\u20322c,\u03bb) ] , (3.7) and n(K)", "mime": "application/pdf"}, {"id": "ejde-196", "words": "7575", "extension": ".pdf", "flesch": "80", "author": "Li, Meiqin; Ji, Bingbing; Zhou, Jianxin", "title": "Local min-orthogonal principle and its applications for solving multiple solution problems", "date": "2023", "keywords": "max; method; min; saddle; type", "summary": "\u2192 p(v) leads to J \u2032(p(vk))\u2192 J \u2032(p(v)) Locally M-type saddles with J > 0 J = 46.1140, \u2016u\u2016\u221e = 4.5370 at (0.0208,\u22120.0104) J = 29.4731, \u2016u\u2016\u221e = 5.7561 at (0.6510,\u22120.0052) J = 17.6390, \u2016u\u2016\u221e = 4.6441 at (0.6458,\u22120.6354) (a)NMO = 15 NMO = 90 NMO = 110 Figure 8.", "mime": "application/pdf"}, {"id": "ejde-1962", "words": "7234", "extension": ".pdf", "flesch": "84", "author": "Wei, Yawei; Zhou, Xiaodong", "title": "Construction of single-peak solutions for Grushin equations via reduction method", "date": "2025", "keywords": "equation; rn+l; solutions; z\u03b5(z; \u2202u\u03b5; \u2202yj", "summary": "= ( 1 (1 + \u03b3)2 |x|2+2\u03b3 + |y|2 ) 1 2+2\u03b3 (1.15) for z = (x, y) \u2208 RN+l, and set B\u0303r(0) : For example, in [2], for u \u2208 D1,2 \u03b3 (RN+l) and \u03c1 > 0, a rescaled sequence of functions of the form ue,\u03c1(z) := \u03c1 N\u03b3\u22122 2 u(\u03c1x, \u03c11+\u03b3y+ e) is also defined, where z = (x, y) \u2208 RN+l and e \u2208 Rl.", "mime": "application/pdf"}, {"id": "ejde-197", "words": "6693", "extension": ".pdf", "flesch": "61", "author": "Mariani, Maria C.; Asante, Peter K.; Kubin, William; Tweneboah, Osei K.; Beccar-Varela, Maria", "title": "Determining the background driving process of the Ornstein-Uhlenbeck model", "date": "2023", "keywords": "analysis; data; differential; equation; le\u0301vy; model; ornstein; process; series; stochastic; time; uhlenbeck", "summary": "[38] proposed the Detrended Fluc- tuation Analysis (DFA) while examining a sequence of DNA nucleotides to study the self-similarity [35] and long-range dependence of time series. The reader is invited to read [3, 32, 42, 43] for further information on the Shan- non entropy, transformation of time series into diffusion processes and the derivation of the shannon entropy for the stationary and non-stationary series.", "mime": "application/pdf"}, {"id": "ejde-1971", "words": "17906", "extension": ".pdf", "flesch": "83", "author": "Kim, Tujin", "title": "Non-steady magneto-hydrodynamics-heat system with joule and buoyancy effects under mixed boundary conditions", "date": "2025", "keywords": "+ k; boundary; conditions; curl; ek1 t; h\u03040; h\u030a(t; problem; t curl; taking; \u2212 \u222b; \u2223\u2223\u2223; \u222b t", "summary": "(4.38) EJDE-2025/119 NON-STEADY MAGNETOHYDRODYNAMICS-HEAT SYSTEMS 19 Taking into account (4.37), (4.38) and applying the inequality |a + b|p \u2264 2p(|a|p + |b|p), p \u2208 (1,\u221e), we have I2 \u2261 1 \u2225u\u2225L6(0,T ;V) \u2223\u2223\u2223 \u222b T 0 [ ek1t\u27e8curl(w\u0302 + v0)\u00d7 (w\u0302 + v0), u\u27e9 ] dt \u2223\u2223\u2223 \u2264 c \u2225u\u2225L6(0,T ;V) \u222b T 0 \u2225 curl(w\u0302 + v0)\u2225L2\u2225(w\u0302 + v0)\u22251/2L2 \u2225(w\u0302 + v0)\u22251/2V \u2225u\u2225L6 dt \u2264 \u2225w\u0302 + v0\u22251/2C(0,T ;L2) ( c \u2225u\u2225L6(0,T ;V) \u2225w\u0302 + v0\u22253/2L9/5(0,T ;V) \u2225u\u2225L6(0,T ;V) ) \u2264 \u2225w\u0302 + v0\u2225C([0,T ];HV) + c\u2225(w\u0302 + v0)\u22253L9/5(0.T ;V) \u2264 c\u2225w\u0302\u2032\u22251/2 L6/5(0,T ;V\u2217) \u2225w\u0302\u22251/2L6(0,T ;V) + \u2225v0\u2225+ c\u2225w\u0302 + v0\u22253L6(0,T ; Let us estimate\u2223\u2223\u2223 \u222b T 0 ek1t\u27e8(w\u0302 + v0)\u03b80,\u2207\u03b8\u0302\u27e9 dt \u2223\u2223\u2223 = \u2223\u2223\u2223 \u222b T 0 [ ek1t\u27e8w\u0302\u03b80,\u2207\u03b8\u0302\u27e9+ ek1t\u27e8v0\u03b80,\u2207\u03b8\u0302\u27e9 ] dt \u2223\u2223\u2223. First, we have\u2223\u2223\u2223 \u222b T 0 ek1t\u27e8w\u0302\u03b80,\u2207\u03b8\u0302\u27e9 dt \u2223\u2223\u2223 \u2264 \u222b T 0 ek1t\u2225w\u0302\u2225L3\u2225\u03b80\u2225L6\u2225\u2207\u03b8\u0302\u2225 dt \u2264 \u03ba0 12 \u2225\u03b8\u0302\u22252 L2(0,T ;W 1,2 \u0393D ) + c\u2032Te4k1T \u03b5 \u2225\u03b80\u22254W 1,2 + \u03b5 6 \u2225w\u0302\u22256L6(0,T ;V).", "mime": "application/pdf"}, {"id": "ejde-198", "words": "9836", "extension": ".pdf", "flesch": "88", "author": "Mavinga, Nsoki; Morris, Quinn A.; Robinson, Stephen B.", "title": "Fucik spectrum with weights and existence of solutions for nonlinear elliptic equations with nonlinear boundary conditions", "date": "2023", "keywords": "lemma; \u03b2(y", "summary": "First, we establish that the functional J is uniformly Lipschitz in \u03b1, \u03b2, and x. Note that |J(\u03b12, \u03b22, x)\u2212 J(\u03b11, \u03b21, x)| = 1 2 \u2223\u2223\u2223(\u03b12 \u2212 \u03b11)\u2016x+\u20162(m,\u03c1) + (\u03b22 \u2212 \u03b21)\u2016x\u2212\u20162(m,\u03c1) \u2223\u2223\u2223 \u2264 1 2\u00b51 \u2016x\u20162(c,\u03c3) (|\u03b12 \u2212 \u03b11|+ |\u03b22 \u2212 \u03b21|) \u2264 1 2\u00b51 K (|\u03b12 \u2212 \u03b11|+ |\u03b22 \u2212 \u03b21|) . = \u2016x2 \u2212 x1\u20162(c,\u03c3) \u2212 \u3008\u03b12x2 \u2212 \u03b11x1, x2 \u2212 x1\u3009(m,\u03c1) + \u3008s2(x2 + y2)\u2212 \u2212 s1(x1 + y1)\u2212, x2 \u2212 x1\u3009(m,\u03c1) = \u2016x2 \u2212 x1\u20162(c,\u03c3) \u2212 \u03b12\u2016x2 \u2212 x1\u20162(m,\u03c1) \u2212 (\u03b12 \u2212 \u03b11)\u3008x1, x2 \u2212 x1\u3009(m,\u03c1) + s2\u3008(x2 + y2)\u2212 \u2212 (x1 + y1)\u2212, x2 \u2212 x1\u3009(m,\u03c1) + (s2 \u2212 s1)\u3008(x1 + y1)\u2212, x2 \u2212 x1\u3009(m,\u03c1) (2.4)", "mime": "application/pdf"}, {"id": "ejde-2", "words": "9827", "extension": ".pdf", "flesch": "85", "author": "Lan, Kunquan", "title": "Linear higher-order fractional differential and integral equations", "date": "2023", "keywords": "solution; \u2208 ac[a; \u2208 c[a", "summary": "If u \u2208 L1(a, b) satisfies (I\u03b1a+(u \u2212 Pn\u22121))(n\u22121) \u2208 AC[a, b], then for each x \u2208 (2) If u \u2208 L1(a, b) satisfies (I\u03b1a+(u\u2212Pn\u22121))(n\u22121) \u2208 AC[a, b] and u is a solution of (3.1)-(3.3), then u is a solution of (3.4)-(3.3).", "mime": "application/pdf"}, {"id": "ejde-20", "words": "3756", "extension": ".pdf", "flesch": "83", "author": "Emamirad, Hassan; Rougirel, Arnaud", "title": "De Bruijn identities in different Markovian channels", "date": "2023", "keywords": "\u03d5(x", "summary": "First we remark that for t = (e2r \u2212 1)/2 = 0, we have e2\u03c4 \u2212 1 = 0, so \u03c4 should be equal zero. \ufe38 =A2(\u03c4) , \u2202 \u2202\u03c4 B(\u03c4, y, \u03be) = ye\u03c4 (e\u03c4y \u2212 \u03be)", "mime": "application/pdf"}, {"id": "ejde-200", "words": "7794", "extension": ".pdf", "flesch": "74", "author": "Takac, Peter", "title": "Nonlinear diffusion with the p-Laplacian in a Black-Scholes-type model", "date": "2023", "keywords": "nonlinear; space", "summary": "= u(log S, t) on the stock price S \u2208 (0,\u221e) for large negative / positive values of the logarithmic stock price x = log S \u2208 R1, i.e., for S \u2192 0+ and S \u2192 +\u221e, respectively. = log S \u2208 R1.", "mime": "application/pdf"}, {"id": "ejde-201", "words": "4379", "extension": ".pdf", "flesch": "74", "author": "Webb, Glenn", "title": "Nonlocal advection diffusion equations and the two-slit experiment in quantum mechanics", "date": "2023", "keywords": "equation; \u03c1(x", "summary": "The interpretation of the solution is that \u222b x2 x1 \u03c1(x, t) dx is the probability of finding a single particle in the interval (x1, x2) at time t, 2. Schro\u0308dinger equation model The one-dimensional time-dependent complex-valued Schro\u0308dinger equation is the foundational phenomenological model of quantum mechanics: \u2202 \u2202t \u03c8(x, t)", "mime": "application/pdf"}, {"id": "ejde-202", "words": "4779", "extension": ".pdf", "flesch": "73", "author": "Amster, Pablo", "title": "A third look at the first result of Landesman-Lazer type", "date": "2021", "keywords": "landesman; lazer; result", "summary": "Summarizing, we have proven that if U := BR(0)\u00d7 (\u2212M,M)n \u2282 R2N then the homotopy h(x, y, s) := (\u222b T 0 g(x+ s(uxy(t)\u2212 x)) dt, s (uxy(T )\u2212 x) + (1\u2212 s)y ) does not vanish on \u2202U . u\u2016L2 because \u222b T 0 \u3008", "mime": "application/pdf"}, {"id": "ejde-203", "words": "3477", "extension": ".pdf", "flesch": "74", "author": "Arango, Jaime", "title": "Oscillation time and damping coefficients in a nonlinear pendulum", "date": "2021", "keywords": "damping; oscillation; time", "summary": "Analogously, for V (t) we obtain V (t) =x0t sin t+ 3ax20 \u222b t 0 cos(t\u2212 s) cos2 sX1(s) ds+O(|x0|4) \u2261V1(t) + V2(t) Notice that x\u03020 \u2264 x0 and the equality holds in the conservative case \u03b1 = 0 only.", "mime": "application/pdf"}, {"id": "ejde-204", "words": "3256", "extension": ".pdf", "flesch": "80", "author": "Acharya, Ananta; Das, Ujjal; Shivaji, Ratnasingham", "title": "Existence and multiplicity results for p-q-Laplacian boundary value problems", "date": "2022", "keywords": "solution", "summary": "We study positive solutions to the boundary value problem \u2212\u2206pu\u2212\u2206qu = \u03bbf(u) in \u2126, u = 0 on \u2202\u2126, where q \u2208 (1, p) and \u2126 is a bounded domain in RN , N > 1 with smooth bound- ary, \u03bb is a positive parameter, and f : Bifurcation diagram for positive solutions to (5.1)", "mime": "application/pdf"}, {"id": "ejde-205", "words": "37869", "extension": ".pdf", "flesch": "81", "author": "Baustian, Falko; Takac, Peter", "title": "Space-time analyticity of weak solutions to semilinear parabolic systems with variable coefficients", "date": "2021", "keywords": "analyticity; cauchy; complex; function; holomorphic; p t; p(rn; problem; r \u2208; solution; space; t \u2208; theorem; time t; u0 \u2208; y t; y \u2208; z \u2208; z0 \u2208; \u2208 bs;p; \u2208 c; \u2208 e1\u2212; \u2208 mrp(e; \u2208 rn; \u2208 u", "summary": "\u2208 RN (or CN ); its coefficients are M \u00d7M matrices (real or complex) which are assumed to be real analytic (jointly) in both variables x \u2208 RN and t \u2208 (0, T ). [0, T ); thus, each X\u03b2(\u00b7, t) (|\u03b2| \u2264 m) belongs to L\u221e(RN ) at every time t \u2208 [0, T ).", "mime": "application/pdf"}, {"id": "ejde-208", "words": "8548", "extension": ".pdf", "flesch": "83", "author": "Chen, Yutong; Su, Jiabao; Sun, Mingzheng; Tian, Rushun", "title": "An elliptic equation involving the square root of the Laplacian without asymptotic limits", "date": "2021", "keywords": "proposition; v(x; \u00b5m+1", "summary": "\u2212 ( \u2016z\u20162 \u2212 \u00b5m \u222b \u2126 |z(x, 0)|2dx ) \u2212 (\u222b {|v(x,0)|<M} + \u222b {|v(x,0)|>M} ) f\u0303(x, v(x, 0))v\u0303(x, 0)dx > ( \u2016w\u20162 \u2212 \u00b5m \u222b \u2126 |w(x, 0)|2dx ) \u2212 ( \u2016z\u20162 \u2212 \u00b5m \u222b \u2126 |z(x, 0)|2dx ) \u2212 \u222b \u2126 (\u00b5m+1 \u2212 \u00b5m \u2212 \u03b5)|w(x, 0)|2dx\u2212 C\u2016v\u0303\u2016 > ( \u00b5m \u00b5m\u22121 \u2212 1 ) \u2016z\u20162 + \u03b5 \u00b5m+1 \u2016w\u20162 \u2212 C\u2016v\u0303\u2016. (4.36) By (4.32) and (4.36), we obtain o(\u2016vn\u2016) = \u3008J \u2032(vn), v\u0303n\u3009 > ( \u00b5m \u00b5m\u22121 \u2212 1 ) 0)|2dx ] \u2212 (\u222b {|v(x,0)|<M} + \u222b {|v(x,0)|>M} ) f\u0303(x, v(x, 0))v\u0303(x, 0)dx > ( 1\u2212 \u00b5m+1 \u00b5m+2 ) \u2016w\u20162 \u2212 [ \u2016z\u20162 \u2212 \u00b5m+1 \u222b \u2126 |z(x, 0)|2dx ] \u2212 \u222b \u2126 (\u00b5m+1 \u2212 \u00b5m \u2212 \u03b5)|z(x, 0)|2dx\u2212 C\u2016v\u0303\u2016 > ( 1\u2212 \u00b5m+1 \u00b5m+2 ) \u2016w\u20162 + \u03b5 \u00b5m \u2016z\u20162 \u2212 C\u2016v\u0303\u2016. (4.18)", "mime": "application/pdf"}, {"id": "ejde-209", "words": "6010", "extension": ".pdf", "flesch": "77", "author": "Calanchi, Marta; Ruf, Bernhard", "title": "Eigenvalues and bifurcation for Neumann problems with indefinite weights", "date": "2021", "keywords": "a(x; existence; problem; solution; \u03bb\u22121", "summary": "\u03c6\u2217, \u03c6 \u2217 two associated eigenvectors, then \u03c6\u2217, \u03c6 \u2217 are orthogonal\u222b \u2126 \u2207\u03c6\u2217\u2207\u03c6\u2217 dx = 0, \u222b \u2126 a(x)\u03c6\u2217\u03c6 \u2217 dx = 0. (b) (First eigenvalues) \u03bb+ 1 = inf u\u2208B+ \u222b \u2126 |\u2207u|2dx \u2265 0, \u03bb\u22121 = \u2212 inf u\u2208B\u2212 \u222b \u2126 |\u2207u|2dx \u2264 0 are simple, with associated positive eigenfunctions \u03c6+ 1 and \u03c6\u22121 . If \u03bb+ 1 := infu\u2208B+ \u222b \u2126 |\u2207u|2dx = 0, there is a sequence un = wn + sn, with \u222b \u2126 wn = 0 and sn \u2208 R such that\u222b \u2126 a(x)u2 n = 1, \u222b \u2126 |\u2207wn|2dx\u2192 0, as n\u2192 +\u221e. Therefore wn \u2192 0 strongly in H1(\u2126) and sn is bounded: otherwise we would have (up to subsequences) 1 = \u222b \u2126 a(x)u2 n = \u222b \u2126 a(x)(s2 n + 2wnsn + w2 n)dx = s2 n (\u222b \u2126 a(x) dx+ o(1) ) \u2192 \u2212\u221e. Since sn is bounded, up to subsequences, sn \u2192 s and un \u2192 s strongly, from which we obtain 1 = \u222b \u2126 a(x)u2 n \u2192 s2 \u222b \u2126 a(x) \u2264 0, which is a contradiction.", "mime": "application/pdf"}, {"id": "ejde-21", "words": "8591", "extension": ".pdf", "flesch": "71", "author": "Zhao, Zhihong; Hu, Huanqin", "title": "Boundedness, stability and pattern formation for a predator-prey model with Sigmoid functional response and prey-taxis", "date": "2023", "keywords": "bifurcation; cos; model; predator; prey; state; system; taxis", "summary": "(3.13) Multiplying the equations of system (3.9) by cos 2i\u03c0x l and then integrating them over 0 to l, once again combining K1 = 0 yields\u222b 1 0 \u03a61 cos 2i\u03c0x l dx = E1 E0 , \u222b 1 0 \u03a81 cos 2i\u03c0x l dx = E2 E0 , (3.14) where E0 = f1g2 \u2212 f2g1 \u2212 4i2\u03c02(\u03bei\u03c7(v\u2217)f2 + g2d1 + f1d2) l2 + 16i4\u03c04d1d2 l4 , E1 = \u03c02i2(\u03beibi\u03c7(v\u2217)f2 + 2M1d2) 2l + (M2f2 \u2212M1g2)l 4 , E2 = \u03c02i2(2\u03bei\u03c7(v\u2217)M1 \u2212 \u03beibi\u03c7(v\u2217)f1 + 2M2d1) 2l + 2\u03c04i4\u03beibi\u03c7(v\u2217)d1 l3 + (M1g1 \u2212M2f1)l 4 , obviously, E0 is always nonzero by \u03bei 6= = (u\u2217 + 0.05 cosx, v\u2217 + 0.05 cosx) and fix \u03be = \u221230, which is obviously far away from the critical bifurcation value.", "mime": "application/pdf"}, {"id": "ejde-211", "words": "5996", "extension": ".pdf", "flesch": "75", "author": "Chhetri, Maya; Mavinga, Nsoki; Pardo, Rosa", "title": "Bifurcation from infinity with oscillatory nonlinearity for Neumann problems", "date": "2022", "keywords": "solutions", "summary": "For each compact set K \u2282 (\u2212\u221e, \u03bb2) \u2282 R, there exists a constant C = C(K), independent of \u03bb \u2208 K, such that \u2016w(\u03bb)\u2016C(\u2126) \u2264 C\u2016g1(\u03bb, \u00b7)\u2016Lr(\u2126) , where w satisfies \u222b \u2126 w = 0 and (2.6), and g1 satisfies (2.4). Therefore, by the Uniform Boundedness Principle, there exists a constant C = C(K) such that \u2016w(\u03bb)\u2016C(\u2126) \u2264 C(K)\u2016g1\u2016Lr(\u2126) for any \u03bb \u2208 K, as desired.", "mime": "application/pdf"}, {"id": "ejde-212", "words": "5712", "extension": ".pdf", "flesch": "78", "author": "Korman, Philip; Schmidt, Dieter S.", "title": "Infinitely many solutions and asymptotics for resonant oscillatory problems", "date": "2022", "keywords": "solutions", "summary": "We derive a rather precise asymptotic formula for \u00b51 = \u00b51(\u03be1) in case |\u03be1| is large, and this formula tends to be accurate for small |\u03be1| as well. Solution curve \u00b51 = \u00b51(\u03be1) of (1.1), oscillating to \u00b1\u221e. Values with |\u00b51| < 1 are not shown. axes), and to make the resulting picture manageable a logarithmic scale is used for both \u03be1 and \u00b51.", "mime": "application/pdf"}, {"id": "ejde-214", "words": "5459", "extension": ".pdf", "flesch": "82", "author": "Ma, Ruyun; Zhao, Zhongzi; Yan, Dongliang", "title": "Connected components of positive solutions of biharmonic equations with the clamped plate conditions in two dimensions", "date": "2021", "keywords": "lemma; solutions; theorem; \u03bb1(a(\u00b7))/f0", "summary": "URL: https://ejde.math.txstate.edu or https://ejde.math.unt.edu CONNECTED COMPONENTS OF POSITIVE SOLUTIONS OF BIHARMONIC EQUATIONS WITH THE CLAMPED PLATE CONDITIONS IN TWO DIMENSIONS RUYUN MA, ZHONGZI ZHAO, DONGLIANG YAN In memory of Professor Alan C. Lazer Abstract. We show the existence of S-shaped connected com- ponent of positive solutions under suitable conditions on the nonlinearity.", "mime": "application/pdf"}, {"id": "ejde-215", "words": "4376", "extension": ".pdf", "flesch": "78", "author": "Mawhin, Jean", "title": "the mean value property and zeros of holomorphic functions (Gauss, Poisson, Bolzano, and Cauchy meet in the complex plane)", "date": "2021", "keywords": "function; holomorphic; reit; theorem", "summary": "Reit (Reit \u2212 z)2 dt and, for z \u2208 DR \\ {0}, g(z)\u2212 g(0) Furthermore, Theorem 3.1 provides a localization z \u2208 DR for the obtained zeros.", "mime": "application/pdf"}, {"id": "ejde-216", "words": "7153", "extension": ".pdf", "flesch": "81", "author": "Maia, Liliane de A.; Oliveira Junior, Jose Carlos; Ruviaro, Ricardo", "title": "Generalized quasilinear equations with critical growth and nonlinear boundary conditions", "date": "2022", "keywords": "g(x; h1(\u03c9; lemma", "summary": "We study the quasilinear problem \u2212 div(h2(u)\u2207u) + h(u)h\u2032(u)|\u2207u|2 + u = \u2212\u03bb|u|q\u22122u+ |u|2\u00b72 \u2217\u22122u in \u2126, \u2202u \u2202\u03b7 = \u00b5g(x, u) on \u2202\u2126, where \u2126 \u2282 R3 is a bounded domain with regular boundary \u2202\u2126, \u03bb, \u00b5 > 0, 1 < q < 4, 2 \u00b72\u2217 = 12, \u2202 \u2202\u03b7 is the outer normal derivative and g has a subcritical growth in the sense of the trace Sobolev embedding. 327 328 L. MAIA, J. C. OLIVEIRA JUNIOR, R. RUVIARO EJDE/SI/01 In this article, we are interested in the quasilinear problem \u2212div(h2(u)\u2207u) + h(u)h\u2032(u)|\u2207u|2 + u = \u2212\u03bb|u|q\u22122u+ |u|2\u00b72 \u2217\u22122u in \u2126, \u2202u \u2202\u03b7 = \u00b5g(x, u) on \u2202\u2126, (1.3) where \u2126 \u2282 R3 is a bounded domain with regular boundary \u2202\u2126, \u03bb, \u00b5 > 0, 1 <", "mime": "application/pdf"}, {"id": "ejde-217", "words": "5037", "extension": ".pdf", "flesch": "78", "author": "Ozturk, Eylem; Rossi, Julio D.", "title": "Limit for the p-laplacian equation with dynamical boundary conditions", "date": "2021", "keywords": "limit; problem", "summary": "\u2200w \u2208 K. When the convex functional \u03a8 : H \u2192 (\u2212\u221e,+\u221e] is proper, lower-semicontinuous, and such that min \u03a8 = 0, it is well known (see [8]) that the abstract Cauchy problem ut + \u2202\u03a8(u) 3 f, a.e. t \u2208 (0, T ), u(0) = u0, has a unique solution for any f \u2208 L1(0, T ;H) and u0 \u2208 D(\u2202\u03a8). Hence, \u222b \u2202\u2126 B(up)(t)\u2212 \u222b \u2202\u2126 B(u0) = \u222b t 0 \u222b \u2202\u2126 \u2202B(up) \u2202t \u2264 \u222b t 0 \u222b \u2202\u2126 f\u03b2(up), here B satisfies B\u2032(s) = \u03b2(s).", "mime": "application/pdf"}, {"id": "ejde-218", "words": "7268", "extension": ".pdf", "flesch": "78", "author": "Pacella, Filomena; Stolnicki, David", "title": "Oscillatory solutions and critical exponents for fully nonlinear equations", "date": "2021", "keywords": "\u2190\u2190 \u2198; \u2191 \u2191; \u2193 \u2198; \u2197 \u2198; \u2198 \u2191; \u2198 \u2197; \u2198 \u2198", "summary": "= F (X,Z) = ( f(X,Z), g(X,Z) ) , (2.5) where the dot \u02d9 stands for derivation with respect to t, and f, g are given by for M+ \u03bb,\u039b: f(X,Z) = { X(X \u2212 (N \u2212 2) + Z \u03bb ) if (X,Z) \u2208 R+ \u03bb X(X \u2212 (N\u0303+ \u2212 2) + Z \u039b ) if (X,Z) \u2208 R\u2212\u03bb , (2.6a) g(X,Z) = { Z(N \u2212 pX \u2212 Z \u03bb ) if (X,Z) \u2208 R+ \u03bb Z(N\u0303+ \u2212 pX \u2212 Z \u039b ) if (X,Z) \u2208 R\u2212\u03bb , (2.6b) (2.6c) and for M\u2212\u03bb,\u039b: f(X,Z) 154 F. PACELLA, D. STOLNICKI EJDE/SI/01 M0 A0 `+ `+2 `+2 `+1 \u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192\u2192 \u2192 \u2192 \u2192 \u2192 \u2192 \u2192 \u2192 \u2192 \u2192 \u2192 \u2192 \u2192 \u2190\u2190 \u2190\u2190 \u2190\u2190 \u2190\u2190 \u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198 \u2197\u2197\u2197\u2197\u2197\u2197\u2197\u2197\u2197\u2197\u2197 \u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198\u2198 \u2191 \u2191 \u2191 \u2191 \u2191 \u2191 \u2191 \u2191 \u2191 \u2191 \u2191 \u2191 \u2191 \u2193\u2193 \u2193 \u2193 \u2193 \u2193 \u2193 \u2193 \u2193 \u2193 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 \u2198 N0 X Z O X = N\u0303+", "mime": "application/pdf"}, {"id": "ejde-219", "words": "5843", "extension": ".pdf", "flesch": "80", "author": "Onete, Florin I.; Papageorgiou, Nikolaos S.; Radulescu, Vicentiu D.", "title": "Twin positive solutions for resonant singular (p,q)-equations", "date": "2021", "keywords": "1,p; papageorgiou", "summary": "(4.32) Now we return to (4.19), choose h = un \u2212 u \u2208 W 1,p 0 (\u2126), pass to the limit as n\u2192\u221e and use (4.32). So, if in (4.23) we choose h = yn \u2212 y \u2208 W 1,p 0 (\u2126), pass to the limit as n \u2192 \u221e and use (4.22), (4.21), (4.24), then we obtain lim n\u2192\u221e \u3008Ap(yn), yn \u2212 y\u3009 = 0, \u21d2 yn \u2192 y in W 1,p 0 (\u2126), hence \u2016y\u2016 = 1, y \u2265 0 (see Proposition 2.1).", "mime": "application/pdf"}, {"id": "ejde-22", "words": "7461", "extension": ".pdf", "flesch": "84", "author": "Daoues, Adel; Hammami, Amani; Saoudi, Kamel", "title": "Multiplicity results of nonlocal singular PDEs with critical Sobolev-Hardy exponent", "date": "2023", "keywords": "p\u2217s(t; |x|t; \u2212 t", "summary": "\u2016v\u03bb\u2016p \u2212 \u03bb ( 1 1\u2212 \u03b1 + 1 p\u2217s(t) )\u222b \u2126 |uk|1\u2212\u03b1 dx+ o(1) \u2265 (sp\u2212 t) p(N \u2212 t) S N\u2212t sp\u2212t + (sp\u2212 t) p(N \u2212 t) \u2016v\u03bb\u2016p \u2212 \u03bb ( 1 1\u2212 \u03b1 + 1 p\u2217s(t) ) |\u2126| p\u2217s (t)\u22121+\u03b1 p\u2217s (t) \u00d7 S\u2212 1\u2212\u03b1 p \u2016v\u03bb\u20161\u2212\u03b1 + o(1) \u2265 (sp\u2212 t) p(N \u2212 t) S N\u2212t sp\u2212t + (sp\u2212 t) p(N \u2212 t)", "mime": "application/pdf"}, {"id": "ejde-220", "words": "8417", "extension": ".pdf", "flesch": "72", "author": "Recova, Leandro L.; Rumbos, Adolfo J.", "title": "An asymmetric problem at resonance with a one-sided Ahmad-Lazer-Paul condition", "date": "2021", "keywords": "g(x; problem", "summary": "Let \u2126 be a bounded, connected, open subset of RN , for N \u2265 2, with smooth boundary \u2202\u2126. Consider the Dirichlet problem \u2212\u2206u = \u03bbku+ g(x, u), x \u2208 \u2126; u = 0, x \u2208 \u2202\u2126, (1.1) where \u03bbk is an eigenvalue of the N -dimensional Laplacian \u2212\u2206 in \u2126 with Dirichlet boundary conditions, and g : \u2126 \u00d7 R \u2192 R is continuous and uniformly bounded; that is, |g(x, s)| 6M, for all x \u2208 \u2126, and s \u2208 R, (1.2) 2010 Mathematics Subject Classification. \u2212 2G(x, um)] dx \u2223\u2223\u2223 6 C + \u03b5m(\u2016u+ m\u2016+ \u2016u\u2212m\u2016), for all m. (3.4) Put T (x, s) = g(x, s)s \u2212 2G(x, s), for x \u2208 \u2126 and s \u2208 R.", "mime": "application/pdf"}, {"id": "ejde-223", "words": "5165", "extension": ".pdf", "flesch": "85", "author": "Yang, Jiaxuan; Li, Yongqing; Wang, Zhi-Qiang", "title": "Radial and non-radial solutions for a nonlinear Schrodinger equation with a constraint", "date": "2021", "keywords": "c(\u03b5; solutions", "summary": "Then c(\u03b5n) = inf \u2016u\u20162=1 (1 2 \u222b RN |\u2207u|2dx\u2212 1 p \u222b RN Q(\u03b5nx)|u|pdx ) \u2264 1 2 \u222b RN |\u2207vn|2dx\u2212 1 p \u222b RN Q(\u03b5nx)|vn|pdx = 1 2 \u222b RN |\u2207vn|2dx\u2212 1 p qM \u222b RN |vn|pdx+ 1 p \u222b RN (qM \u2212Q(\u03b5nx))|vn|pdx 230 J. YANG, Y. LI, Z.-Q. WANG EJDE/SI/01 = cqM + 1 p \u222b RN (qM \u2212Q(\u03b5nx))|vn|pdx. lim sup \u03b5\u21920 c(\u03b5, k) \u2264 c k 2\u2212p 2 qM (4.4) where as in (1.5), c k 2\u2212p 2 qM = inf u\u2208H1,\u2016u\u20162=1 (1 2 \u222b R2 |\u2207u|2dx\u2212 k 2\u2212p 2 qM p \u222b R2 |u|pdx ) .", "mime": "application/pdf"}, {"id": "ejde-224", "words": "5314", "extension": ".pdf", "flesch": "82", "author": "Simsen, Jacson", "title": "Evolution equations on time-dependent Lebesgue spaces with variable exponents", "date": "2023", "keywords": "d\u03bb(t; p(x; p(\u00b7,t", "summary": "The family of pullback attractors {A\u03bb(t) : t \u2208 R}, \u03bb \u2208 [0,\u221e) is upper semicontinuous at \u03bb1 in the topology of H. Proof. For t \u2208 R and \u03b5 > 0, let \u03c4 \u2208 R be such that distYt ( U\u03bb1(t, \u03c4)B(\u03c4),A\u03bb1(t) ) < \u03b5 3 , where \u222a\u03bb\u2208[0,\u221e)A\u03bb(\u03c4) \u2282 B(\u03c4) and B(\u03c4) is a nonempty set in X\u03c4 \u2282", "mime": "application/pdf"}, {"id": "ejde-225", "words": "4278", "extension": ".pdf", "flesch": "74", "author": "Ahrami, Mohammed; El Allali, Zakaria", "title": "Lower bounds on the fundamental spectral gap with Robin boundary conditions", "date": "2022", "keywords": "boundary; gap; robin; schro\u0308dinger", "summary": "Our main results include improvements of the lower bound on the fundamental gap of Robin Schro\u0308dinger operators with a convex potential. [6] M. Ashbaugh, D. Kielty; spectral gaps of 1-D Robin Schro\u0308dinger operators with single-well potentials, Journal of Mathematical Physics, 61, 091507 (2020).", "mime": "application/pdf"}, {"id": "ejde-226", "words": "8717", "extension": ".pdf", "flesch": "82", "author": "Awanou, Gerard", "title": "Discrete Aleksandrov solutions of the Monge-Ampere equation", "date": "2022", "keywords": "aleksandrov; convergence; convex; function; monge; proof; solution; viscosity", "summary": "Let x0 \u2208 \u2126 and \u03c6 be a strictly convex quadratic polynomial such that u\u2217 \u2212 \u03c6 has a local minimum at x0 with (u\u2217 \u2212 \u03c6)(x0) = 0. For x \u2208 \u2126 we denote by d(x, \u2202\u2126) the distance of x to \u2202\u2126. For a subset S of \u2126, diam(S) denotes its diameter. Lemma 2.11.", "mime": "application/pdf"}, {"id": "ejde-228", "words": "4872", "extension": ".pdf", "flesch": "70", "author": "Cho, Manki; Rivas, Mauricio A.", "title": "On the L^2-orthogonality of Steklov eigenfunctions", "date": "2022", "keywords": "eigenfunctions; orthogonality; steklov; \u03c91\u03b1", "summary": "A consequence of the calculations is a tabulation of the mean value of Steklov eigenfunctions over \u21261\u03b1. Introduction This article describes the exact, or near, orthogonality in L2(\u21261\u03b1) of the sequence of Steklov eigenfunctions in the case \u21261\u03b1 is a rectangle in R2.", "mime": "application/pdf"}, {"id": "ejde-229", "words": "17555", "extension": ".pdf", "flesch": "69", "author": "Feng, Xiaobing; Lewis, Thomas; Ward, Kellie", "title": "A narrow-stencil framework for convergent numerical approximations of fully nonlinear second order PDEs", "date": "2022", "keywords": "boundary; i=1; numerical; operators; order", "summary": "Then F\u03020, F\u0303ij , and \u2212F\u0302ij are all nonnegative definite, and we have (5.10) becomes W\u0302 = (I \u2212 \u03c1F\u03020)W \u2212 \u03c1 d\u2211 i=1 d\u2211 j=1 ( F\u0303ij + F\u0302ij ) \u2212 F\u0302 ( D\u03022 hk uhk (xk), D\u03022 hk uhk (xk), uhk (xk),xk ) . (4.5) Then, by the mean value theorem, the Lipschitz continuity of F , and the uniform and proper ellipticity of F , there exists a constant K \u2265 0", "mime": "application/pdf"}, {"id": "ejde-230", "words": "6752", "extension": ".pdf", "flesch": "72", "author": "Guo, Daniel X.", "title": "Semi-Lagrangian forward methods for some time-dependent nonlinear partial differential equations", "date": "2022", "keywords": "k d; k d2; method; x k", "summary": "Semi-Lagrangian methods have been introduced at the beginning of the eighties Recently, more applications of semi-Lagrangian method are reported.", "mime": "application/pdf"}, {"id": "ejde-232", "words": "7283", "extension": ".pdf", "flesch": "73", "author": "Lewis, Thomas; Rapp, Aaron; Zhang, Yi", "title": "Penalty parameter and dual-wind discontinuous Galerkin approximation methods for elliptic second order PDEs", "date": "2022", "keywords": "dwdg; error; solution; u \u03b3; \u2212 u", "summary": "By the Cauchy-Schwarz inequality and the fact that [[uch \u2212 u]]e = 0 for all e \u2208 Eh, we have Bh,\u03b3(uch \u2212 u, uch \u2212 u \u03b3 h) \u2264 1 2 \u2016\u2207+ h,0(uch \u2212 u)\u2016L2(Th)\u2016\u2207+ h,0(uch \u2212 u \u03b3 h)\u2016L2(Th) + 1 2 \u2016\u2207\u2212h,0(uch \u2212 u)\u2016L2(Th)\u2016\u2207\u2212h,0(uch \u2212 u \u03b3 h)\u2016L2(Th) + \u03b3 \u2211 e\u2208Eh \u3008h\u22121 e [[uch \u2212 u \u03b3 h]]\u20162L2(e) \u2264 Bh,\u03b3(uch \u2212 u \u03b3 h, u c h \u2212 u \u03b3 h) = Bh,\u03b3(uch \u2212 u, uch \u2212 u \u03b3 h) +Bh,\u03b3(u\u2212 u\u03b3h, u c h \u2212 u \u03b3 h).", "mime": "application/pdf"}, {"id": "ejde-234", "words": "9910", "extension": ".pdf", "flesch": "70", "author": "Valdebenito, Dario A.", "title": "On solutions arising from radial spatial dynamics of some semilinear elliptic equations", "date": "2022", "keywords": "equation; form; hamiltonian; sn\u22121; solutions; terms; theorem", "summary": "Previ- ously, related ideas for finding quasiperiodic solutions of elliptic equations on an unbounded strip have been used by Scheurle [38] P. Pola\u0301c\u030cik, D. Valdebenito; Existence of quasiperiodic solutions of elliptic equations on RN+1 via center manifold and KAM theorems, Journal of Differential Equations 262 (2017), 6109\u2013 6164.", "mime": "application/pdf"}, {"id": "ejde-235", "words": "6041", "extension": ".pdf", "flesch": "84", "author": "Huang, Lan-Xin; Wu, Xing-Ping; Tang, Chun-Lei", "title": "Multiple positive solutions for nonhomogeneous Schrodinger-Poisson systems with Berestycki-Lions type conditions", "date": "2021", "keywords": "system", "summary": "Repeating the proof of Lemma 2.2, we easily obtain on(1) = \u3008I \u2032\u03bb,T (un)\u2212 I \u2032\u03bb,T (u), un \u2212 u\u3009 \u2265 min{1,m}\u3008un, un \u2212 u\u3009 \u2212max{1,m}\u3008u, un \u2212 u\u3009 + \u03bbhT (un) \u222b R3 \u03c6unun(un \u2212 u) dx\u2212 \u03bbhT (u) \u222b R3 \u03c6uu(un \u2212 u) dx + a\u03bb,T (un) 2 \u3008un, un \u2212 u\u3009 \u2212 a\u03bb,T (u) 2 \u3008u, un \u2212 u\u3009 \u2212 \u222b R3 (g1(un)\u2212 g1(u))(un \u3008un, un \u2212 u\u3009, 8 L.-X. HUANG, X.-P. WU, C.-L. TANG EJDE-2021/01 this shows that ( min{1,m} + a\u03bb,T (un) 2 ) \u3008un, un \u2212 u\u3009 \u2192 0 as n \u2192 \u221e. By (2.2) and (3.2), we have |a\u03bb,T (un)| \u2264 \u03bbT\u22122|\u03c7\u2032(T\u22122\u2016un\u20162)| \u2223\u2223 \u222b R3 \u03c6unu 2 n dx \u2223\u2223 < 8\u03bbT\u0303 .", "mime": "application/pdf"}, {"id": "ejde-236", "words": "7006", "extension": ".pdf", "flesch": "80", "author": "Engu, Satyanarayana; Sahoo, Manas R.; Berke, Venkatramana P.", "title": "Solutions to viscous Burgers equations with time dependent source term", "date": "2021", "keywords": "burgers; equation; solutions", "summary": "\u222b 0 \u2212\u221e \u2212wwt dx dt+ \u222b 0 \u2212\u221e w2(x, t) dx \u2212 1 2 [ \u222b T 0 \u222b 0 \u2212\u221e (u+ v)wwx dx dt\u2212 \u222b T 0 (w (u+ v)w)(0, t) dt ] + \u222b T 0 \u222b 0 \u2212\u221e w2 x dx dt\u2212 \u222b T 0 (wxw)(0, t) dt = 0. (3.8) Similarly for \u03c6 = w(x, t)H(T \u2212 t)H(x), integral equation (3.7) yields\u222b T 0 \u222b \u221e 0 \u2212wwt dx dt+ \u222b \u221e 0 w2(x, t) dx + \u222b T 0 \u222b R w2 x dx dt+ \u222b T 0 [ (wxw)(0+, t)\u2212 (wxw)(0\u2212, t) ] dt = 1 2 [ \u222b T 0 \u222b R (u+ v)wwx dx dt+ \u222b T 0 [ ((u+ v)w2)(0+, t)\u2212 ((u+ v)w2)(0\u2212, t) ] dt ] , which implies \u2016w(\u00b7, T )\u201622 + 2 \u222b T 0 \u2016wx(\u00b7 , t)\u201622 dt \u2264 1 2 \u222b T 0 \u222b R \u2016(u+ v)(t)\u2016\u221e|w(x, t)\u2016wx(t)| dx dt \u2264 1 2 \u222b T 0 \u2016(u+", "mime": "application/pdf"}, {"id": "ejde-237", "words": "7844", "extension": ".pdf", "flesch": "91", "author": "Ali, Mageed; Iaia, Joseph A. Iaia", "title": "Existence and nonexistence for singular sublinear problems on exterior domains", "date": "2021", "keywords": "1+q; 2\u2212\u03b1\u0303; r2\u2212n", "summary": "ds \u2265 \u222b t 0 h(s) ds. (2.15) Integrating (2.15) again and using (2.7) gives vq+1 a (t) q + 1 + \u222b t 0 \u222b ds = \u222b t 0 h(s) ds.", "mime": "application/pdf"}, {"id": "ejde-238", "words": "4623", "extension": ".pdf", "flesch": "73", "author": "Sourdis, Christos", "title": "An asymptotic monotonicity formula for minimizers of elliptic systems of Allen-Cahn type and the Liouville property", "date": "2021", "keywords": "solutions; theorem", "summary": "In light of the recent density estimates of [23], we expect that the assertions of Theorems 1.1 and 1.2 should also remain valid under the complementary set of assumptions that W \u2208 C1 satisfies c|u\u2212 a|p \u2264W (u) \u2264 C|u\u2212 a|p, u \u2208 Rm, m \u2265 1, for some constants c, C > 0, where p \u2208 { (2,\u221e), n = 2,( 2, 2n n\u22122 ) , n \u2265 3. (2.8) From (2.2), using again that W \u2208 C1, there exists a C4 > 0 such that \u2016e\u2016C0,\u03b1(Rn;R) \u2264 C4.", "mime": "application/pdf"}, {"id": "ejde-239", "words": "7081", "extension": ".pdf", "flesch": "89", "author": "He, Rui; Liu, Xiangqing", "title": "Localized nodal solutions for parameter-dependent quasilinear Schrodinger equations", "date": "2021", "keywords": "1,m; \u03c7\u03b5(x)u2; \u222b rn", "summary": "It holds that (1) p \u00b7A(z, p) \u2265 \u03c6(K)g\u00b5(|p|)|p|, (2) |A(z, p)| \u2264 \u03a6(K)g\u00b5(|p|), (3) |B(x, z, p)| \u2264 \u03a6(K)(1 + g\u00b5(|p|)|p|) for x \u2208 RN , z \u2208 R, |z| \u2264 K, p \u2208 RN , where \u03c6, \u03a6 are two functions from R+ to R+ such that \u03c6 is decreasing and \u03a6 is increasing. \u2212 V (x)v + \u03bb|v|q\u22122v = 0, v(x)\u2192 0 as |x| \u2192 \u221e, (1.1) where x \u2208 RN , \u03b5 > 0 is a small parameter, Div = \u2202v \u2202xi , Dzbij(z)", "mime": "application/pdf"}, {"id": "ejde-240", "words": "6658", "extension": ".pdf", "flesch": "82", "author": "Antontsev, Antontsev; Ferreira, Jorge; Piskin, Erhan", "title": "Existence and blow up of solutions for a strongly damped Petrovsky equation with variable-exponent nonlinearities", "date": "2021", "keywords": "equation; solutions; \u2016ut\u20162", "summary": "= \u222b \u2126 |u|q(\u00b7)dx (5.6) for any u \u2208 H2 0 (\u2126) and 2 \u2264 s \u2264 q\u2212. Where C > 1 a positive constant and H(t) = \u2212E(t). = (1\u2212 \u03c3)H\u2212\u03c3(t)H \u2032(t) + \u03b5 \u222b \u2126 (u2 t + uutt)dx+ \u03b5 \u222b \u2126 \u2207u\u2207ut dx = (1\u2212 \u03c3)H\u2212\u03c3(t)H \u2032(t) + \u03b5\u2016ut\u20162 \u2212 \u03b5\u2016\u2206u\u20162 + \u03b5 \u222b \u2126 |u|q(\u00b7)dx\u2212 \u03b5 \u222b \u2126 uut|ut|p(\u00b7)\u22122dx. (5.13) By using the definition of the H(t), it follows that \u2212\u03b5q\u2212(1\u2212 \u03be)H(t) = \u03b5q\u2212(1\u2212 \u03be) 2 \u2016ut\u20162 + \u03b5q\u2212(1\u2212 \u03be) 2 \u2016\u2206u\u20162 \u2212 \u03b5q\u2212(1\u2212 \u03be) \u222b \u2126 1 q(x) |u|q(\u00b7)dx, (5.14) where 0 < \u03be < 1.", "mime": "application/pdf"}, {"id": "ejde-241", "words": "8588", "extension": ".pdf", "flesch": "86", "author": "Liu, Lintao; Teng, Kaimin", "title": "Ground state and multiple solutions for critical fractional Schrodinger-Poisson equations with perturbation terms", "date": "2021", "keywords": "fractional; lemma; sdx; solutions; \u222b r3", "summary": "(3.3) Let R > 0 and \u03b3 \u2208 R3 with |\u03b3| = 1. = I(tu\u221e(x \u2212 R\u03b3)), t \u2208 (0,\u221e), \u03b3 \u2208 R3 with |\u03b3| = 1.", "mime": "application/pdf"}, {"id": "ejde-242", "words": "8282", "extension": ".pdf", "flesch": "76", "author": "Diaz, Jesus Ildefonso; Hilhorst, Danielle; Kyriazopoulos, Paris", "title": "A parabolic system with strong absorption modeling dry-land vegetation", "date": "2021", "keywords": "problem; solution; system", "summary": "Now, let x0 \u2208 \u2126 \u2212 supp(h0), R : (2.6) In any case, we are specifically interested in the case in which the initial data satisfy 0 \u2264 b0 \u2264 1, w0 \u2265 0, h0 \u2265 0, on \u2126. (2.7) Concerning the precipitation term p, we assume that p \u2208 L\u221e(QT ) is nonnegative.", "mime": "application/pdf"}, {"id": "ejde-243", "words": "15385", "extension": ".pdf", "flesch": "82", "author": "Giacomoni, Jacques; Gouasmia, Abdelhamid; Mokrane, Abdelhafid", "title": "Existence and global behavior of weak solutions to a doubly nonlinear evolution", "date": "2021", "keywords": "f(x; fractional; problem; solution; theorem; vq\u22121; w s; y|n+sp; |x\u2212; \u03b5)q; \u03b5)q\u22121; \u222b rn; \u222b \u03c9", "summary": "= ( \u2016u\u2016p Lp(RN ) + \u222b RN \u222b RN |u(x)\u2212 u(y)|p |x\u2212 y|N+sp dx dy )1/p . \u2022 The space W s,p 0 (\u2126) is the set of functions W s,p 0 (\u2126) := {u \u2208W s,p(RN ) : u = 0 a.e. in RN \\ \u2126}, and the norm is given by the Gagliardo semi-norm \u2016u\u2016W s,p 0 (\u2126) := (\u222b RN \u222b RN |u(x)\u2212 u(y)|p |x\u2212 y|N+sp dx dy )1/p . Then, for any r \u2265 1, \u2016vq(t, \u00b7)\u2212 vq\u221e\u2016Lr(\u2126) \u2192 0 as t\u2192\u221e, where v\u221e is the unique stationary solution to (1.12) associated to the potential h\u221e. This article is organized as follows: In Section 2, we study the stationary non- linear problem v2q\u22121 + \u03bb(\u2212\u2206)spv = h0(x)vq\u22121 + \u03bbf(x, v) in \u2126, v > in \u2126, v = 0 in RN \\ \u2126, related to the parabolic problem (1.12) and establish the existence and the unique- ness results in case h0 \u2208 L\u221e(\u2126)", "mime": "application/pdf"}, {"id": "ejde-244", "words": "4390", "extension": ".pdf", "flesch": "84", "author": "Ciou, Jyun-Yuan; Tzung-Shin, Tzung-Shin", "title": "Complete classification of bifurcation curves for a multiparameter diffusive logistic problem with generalized Holling type-IV functional response", "date": "2021", "keywords": "bifurcation; curve", "summary": "In this article we study exact multiplicity of positive solutions and shapes of bifurcation curves of (1.1) for parameters m \u2265 1 and q, r > 0. We divide the first quadrant of (q, r)- parameter plane into the disjoint union of three curves \u03931, \u03932, \u03933 and five regions EJDE-2021/10 BIFURCATION CURVES FOR A DIFFUSIVE LOGISTIC PROBLEM 5 R1, R2, R3, R4, R5 defined as follows: \u03931 = { (q, r) : q(a)", "mime": "application/pdf"}, {"id": "ejde-245", "words": "6726", "extension": ".pdf", "flesch": "80", "author": "Cui, Na; Sun, Hong-Rui", "title": "Existence of solutions for critical fractional p-Laplacian equations with indefinite weights", "date": "2021", "keywords": "fractional", "summary": "Then it follows that \u03ben(x, y)\u2192 |u(x)\u2212u(y)|p\u22122(u(x)\u2212u(y)) |x\u2212y| N+sp p\u2032 a.e. in RN \u00d7 RN . \u03b5 ( [v\u03b5,\u03c1] p s,p \u2212 \u03bb \u222b RN g|v\u03b5,\u03c1|p dx ) \u2212 tp \u2217 s\u22121 \u03b5 \u222b RN h|v\u03b5,\u03c1|p \u2217 s dx, moreover, combining (A2), (A3) and (A4), we deduce that t p\u2217s\u2212p \u03b5 = [v\u03b5,\u03c1] p s,p \u2212 \u03bb \u222b RN g|v\u03b5,\u03c1| p dx\u222b RN h|v\u03b5,\u03c1|p \u2217 s dx \u2264", "mime": "application/pdf"}, {"id": "ejde-246", "words": "10036", "extension": ".pdf", "flesch": "84", "author": "Papageorgiou, Nikolaos S.; Vetro, Calogero; Vetro, Francesca", "title": "Multiple solutions for semilinear Robin problems with superlinear reaction and no symmetries", "date": "2021", "keywords": "f\u03bb(z; h1(\u03c9; intc+", "summary": "So, if there exists M > 0 such that for a.a. z \u2208 \u2126 x 7\u2192 f\u03bb(z, x) x is nondecreasing on [M,+\u221e), 6 N. S. PAPAGEORGIOU, C. VETRO, F. VETRO EJDE-2021/12 x 7\u2192 f\u03bb(z, x) x is nonincreasing on (\u2212\u221e,\u2212M ], then the quasimonotonicity condition (H2)(iii) is satisfied. Let \u2126+ = {z \u2208 \u2126 : y(z) > 0}.", "mime": "application/pdf"}, {"id": "ejde-248", "words": "5179", "extension": ".pdf", "flesch": "79", "author": "Maione, Alberto", "title": "H-convergence for equations depending on monotone operators in Carnot groups", "date": "2021", "keywords": "operators", "summary": "Let f \u2208 V \u2217 and let B : V \u2192 V \u2217 be defined by \u3008B(u), v\u3009V \u2217\u00d7V := \u222b \u2126 ( \u3008A(x,\u2207Gu),\u2207Gv\u3009 \u2212 f v ) dx \u2200u, v \u2208 V. Let us show that B is strictly-monotone, coercive and continuous on any finite dimensional subspace of V . The class M(\u03b1, \u03b2; \u2126) is defined as follows.", "mime": "application/pdf"}, {"id": "ejde-249", "words": "12530", "extension": ".pdf", "flesch": "86", "author": "Yang, Zhipeng; Zhang, Wei; Zhao, Fukun", "title": "Existence and concentration results for fractional Schrodinger-Poisson system via penalization method ", "date": "2021", "keywords": "fractional; lemma; poisson; proof; schro\u0308dinger; solutions", "summary": "Note that un satisfies (\u2212\u2206)sun + un = \u03a5n, x \u2208 R3, where \u03a5n(x) = un(x)\u2212 V (\u03b5n(x+ y\u0303n))un(x)\u2212 \u03c6tunun(x) + g(\u03b5n(x+ y\u0303n), un), x \u2208 R3. The fractional Laplacian, (\u2212\u2206)\u03b1u, of a smooth function u : R3 \u2192 R, is defined by F((\u2212\u2206)\u03b1u)(\u03be) = |\u03be|2\u03b1F(u)(\u03be), \u03be \u2208 R3.", "mime": "application/pdf"}, {"id": "ejde-25", "words": "5782", "extension": ".pdf", "flesch": "82", "author": "Jiang, Shuai; Yin, Li-Feng", "title": "Existence of nontrivial solutions for Schrodinger-Kirchhoff equations with indefinite potentials", "date": "2023", "keywords": "|\u2207u|2", "summary": "= \u222b t 0 g(\u03c4)d\u03c4 \u2265 c|t|\u03bd for some \u03bd < 4, then problem (1.6) has at least one nontrivial solution. (2.16) We write the integral over R3 \\BR as the sum of the integrals over the intersections of R3 \\ BR with {V \u2265 0} and {V < 0}.", "mime": "application/pdf"}, {"id": "ejde-252", "words": "3177", "extension": ".pdf", "flesch": "86", "author": "Fan, Jishan; Zhou, Yong", "title": "Uniform regularity of fully compressible Hall-MHD systems", "date": "2021", "keywords": "div; rot", "summary": "[1 2 \u2207|D3b|2 \u2212 (D3b \u00b7 \u2207)D3b ] udx + \u03be \u222b ( D3 ( b \u03c1 \u00d7 rot b ) \u2212 b \u03c1 \u00d7D3 rot b ) D3 rot bdx = \u2212 \u222b rot(D3(b\u00d7 u)\u2212D3b\u00d7 u\u2212 b\u00d7D3u)D3bdx EJDE-2021/17 FULLY COMPRESSIBLE HALL-MHD SYSTEMS 7 \u2212 1 2 \u222b |D3b|2 div udx+ \u222b D3b\u2297D3b : \u2207udx + \u03be \u222b ( D3 ( b \u03c1 \u00d7 rot b ) \u20161 \u03c1 \u2016Lq\u2016 div u\u2016L\u221e , which gives \u20161 \u03c1 \u2016Lq \u2264 \u2016 1 \u03c10 \u2016Lq exp (( 1 + 1 q ) \u222b t 0 \u2016 div u\u2016L\u221ed\u03c4 )", "mime": "application/pdf"}, {"id": "ejde-253", "words": "4737", "extension": ".pdf", "flesch": "75", "author": "Chen, Yu Xian; Xu, Hong Yan", "title": "Exact forms of entire solutions for Fermat type partial differential equations in C^2", "date": "2021", "keywords": "differential; equations; solutions; \u2202z1", "summary": "= sin(z2 \u2212 z1 + \u03b71)\u2212 cos(z2 \u2212 z1 + \u03b71) + \u03b72e \u2212(z1+z2), where \u03b7, \u03b71, \u03b72 \u2208 C. Secondly, we study the existence and the form of transcendental entire solutions of several second order partial differential equations of Fermat type,[ a1f(z) + a2 \u2202f \u2202z1 ]2 + URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu EXACT FORMS OF ENTIRE SOLUTIONS FOR FERMAT TYPE PARTIAL DIFFERENTIAL EQUATIONS IN C2 YU XIAN CHEN, HONG YAN XU Abstract.", "mime": "application/pdf"}, {"id": "ejde-254", "words": "8843", "extension": ".pdf", "flesch": "84", "author": "Pu, Hongling; Li, Shiqi; Liang, Sihua; Repovs, Dusan D.", "title": "Nodal solutions of fourth-order Kirchhoff equations with critical growth in R^N", "date": "2021", "keywords": "i\u03bbb; kirchhoff; problem; solutions", "summary": "Then for any u \u2208 E with u\u00b1 6= 0, there is the unique maximum point pair of positive numbers (\u03b1u, \u03b2u) such that \u03b1uu + + \u03b2uu \u2212 \u2208 N \u03bb b . Proof. [22], together with (2.6) and (2.8), we can conclude that there exists (\u03b1u, \u03b2u) \u2208 R+\u00d7R+ such that W (\u03b1u, \u03b2u) = (0, 0), i.e., \u03b1uu + + \u03b2uu \u2212 \u2208 N \u03bb b .", "mime": "application/pdf"}, {"id": "ejde-255", "words": "3354", "extension": ".pdf", "flesch": "83", "author": "Allahverdiev, Bilender P.; Tuna, Huseyin; Isayev, Hamlet A", "title": "Impulsive regular q-Dirac systems", "date": "2023", "keywords": "\u03bb)h1(qt", "summary": "\u03c721(qt, \u03bb)h2(qt))dqt + q \u03c9(\u03bb)\u03c811(\u03be, \u03bb)\u03b1 \u222b a d (\u03c712(qt, \u03bb)h1(qt) + \u03c722(qt, \u03bb)h2(qt))dqt, \u03be \u2208 I1, q \u03c9(\u03bb)\u03c712(\u03be, \u03bb) \u222b \u03c721(qt, \u03bb)h2(qt))dqt + q \u03c9(\u03bb)\u03c821(\u03be, \u03bb)\u03b1 \u222b a d (\u03c712(qt, \u03bb)h1(qt) + \u03c722(qt, \u03bb)h2(qt))dqt, \u03be \u2208 I1, q \u03c9(\u03bb)\u03c722(\u03be, \u03bb) \u222b", "mime": "application/pdf"}, {"id": "ejde-256", "words": "7121", "extension": ".pdf", "flesch": "82", "author": "Barboza, Eudes M.; Miyagaki, Olimpio H.; Pereira, Fabio R.; Santana, Claudia R.", "title": "Henon equation with nolinearities involving Sobolev critical growth in H^1", "date": "2021", "keywords": "0,rad(b1; 2\u2217\u03b1", "summary": "Here H1 0,rad(B1) = {u \u2208 H1 0 (B1) : u is radial, that is, u(x) = u(|x|),\u2200x \u2208 B1}. First of all, we define W (\u03b5, r) = {u \u2208 H1 0,rad(B1);u = u\u2212 + tur\u03b5 , u \u2212 \u2208 H2, t \u2208 R}.", "mime": "application/pdf"}, {"id": "ejde-257", "words": "5430", "extension": ".pdf", "flesch": "83", "author": "Pereira, Ducival; Cordeiro, Sebastiao; Raposo, Carlos; Maranhao, Celsa", "title": "Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity", "date": "2021", "keywords": "equation; |u|2", "summary": "Integrating (3.7) from 0 to t, 0 \u2264 t \u2264 tm, we obtain 1 2 \u2016umt (t)\u20162 + 1 2 \u2016\u2206um(t)\u20162 + 1 2 M\u0302(\u2016\u2207um(t)\u20162) + 1 2 \u2016um(t)\u20162 + \u222b t 0 \u2016umt (s)\u20162ds = 1 2 \u2016u1m\u20162 + 1 2 \u2016\u2206u0m\u20162 + 1 2 M\u0302(\u2016\u2207u0m\u20162)\u2212 1 2 \u222b \u2126 (u0m)2 ln |u0m|2 dx (3.8) + 1 2 \u222b \u2126 (um(t))2 ln |um(t)|2 dx. Introduction In this article we study the existence and decay properties of global solutions for the nonlinear initial boundary value problem utt + \u22062u+M(\u2016\u2207u\u20162)(\u2212\u2206u)", "mime": "application/pdf"}, {"id": "ejde-258", "words": "10054", "extension": ".pdf", "flesch": "78", "author": "Han, Bang-Sheng; Kong , De-Yu Kong; Shi, Qihong; Wang, Fan", "title": "Periodic traveling waves and asymptotic spreading of a monostable reaction-diffusion equations with nonlocal effects", "date": "2021", "keywords": "equation; solutions; state; steady; wave", "summary": "The map h has the form h(|B|2, \u03b5, \u03b4) =\u2212 \u03c6\u0302(\u03c3c) 2 \u03b52 \u2212 ( 1 + 1 + \u03b1c \u2212 \u03b2c 2 \u03c6\u0302\u2032\u2032(\u03c3c) ) \u03b42 + \u03c2|B|2 +O(|\u03b4|3 + |\u03b5|2|\u03b4|+ |B|4), (2.9) where \u03c2 :=\u2212 2(1 + \u03b1c \u2212 \u03b2c)\u03c6\u0302(\u03c3c)\u2212 2(\u03b1c \u2212 3\u03b2c) 1 + \u03b2c ( \u03b1c \u2212 1\u2212 5\u03b2c + \u03c6\u0302(\u03c3c) ) + \u03b1c \u2212 3\u03b2c \u2212 (1 + \u03b1c \u2212 \u03b2c)\u03c6\u0302(\u03c3c) 4\u03c32 c \u2212 (\u03b1c \u2212 2\u03b2c) + (1 + \u03b1c \u2212 \u03b2c)\u03c6\u0302(2\u03c3c) (5.1) 20 B.-S. HAN, D.-Y. KONG, Q. SHI, F. WANG EJDE-2021/22 Substituting (5.1) into (2.7) and comparing the coefficient of B2ei2x and BB, we have e2,0 = \u03b1c \u2212 3\u03b2c \u2212 (1 + \u03b1c \u2212 \u03b2c)\u03c6\u0302(\u03c3c) 4\u03c32 c \u2212 (\u03b1c \u2212 2\u03b2c) + (1 + \u03b1c \u2212 \u03b2c)\u03c6\u0302(2\u03c3c) ei2x + span(e, e\u0304), and e1,1 = 2(1 + \u03b1c \u2212 \u03b2c)\u03c6\u0302(\u03c3c)\u2212", "mime": "application/pdf"}, {"id": "ejde-259", "words": "10426", "extension": ".pdf", "flesch": "90", "author": "Zhang, Yajing; Li, Qiaoqin; Pang, Lu", "title": "Existence of multiple positive solutions for fractional Laplace problems with critical growth", "date": "2021", "keywords": "lemma", "summary": "\u2212 u0 \u2212 \u2211\u0300 j=1 (rjn) 2s\u2212N 2 uj (x\u2212 xjn rjn )\u2225\u2225 H\u0307(RN ) Moreover, either the convergence is strong, or there exist ` \u2208 N, nontrivial solutions u1, . . .", "mime": "application/pdf"}, {"id": "ejde-260", "words": "5024", "extension": ".pdf", "flesch": "89", "author": "Ren, Yuanyuan; Li, Yongsheng", "title": "Small data blow-up of solutions to nonlinear Schrodinger equations without gauge invariance in L^2", "date": "2021", "keywords": "solution", "summary": "Then there exist a positive time T = T (\u03b5, \u2016f\u2016L2 , \u2016g\u2016L2) and a unique solution (u, v) \u2208 XT\u00d7XT of (2.1). \u2223\u2223 \u222b [0,T )\u00d7Rn (|u|p1 \u2212 |uk|p1)\u03c8 dx dt \u2223\u2223+ \u2223\u2223 \u222b [0,T )\u00d7Rn (|v|p2 \u2212 |vk|p2)\u03c8 dx dt \u2223\u2223 .", "mime": "application/pdf"}, {"id": "ejde-263", "words": "11725", "extension": ".pdf", "flesch": "86", "author": "Youssfi, Ahmed; Khatri, Mohamed Mahmoud Ould", "title": "Continuous imbedding in Musielak spaces with an application to anisotropic nonlinear Neumann problems", "date": "2021", "keywords": "function; musielak; u(x; \u03c6(\u03c9", "summary": ", N , we denote by \u03bdi the ith component of the outer normal unit vector and ai : \u2126 \u00d7 R \u2192 R is a Carathe\u0301odory function such that there exist a locally integrable Musielak-Orlicz function (see definition 1.1 below) Pi : \u2126\u00d7 R+ \u2192 R+ with Pi \ufffd \u03c6i, a positive constant ci and a nonnegative function di \u2208 E\u03c6\u2217i (\u2126) satisfying for all s, t \u2208 R and for almost every x \u2208 \u2126 the following assumptions |ai(x, s)| \u2264 ci ( di(x) + (\u03c6\u2217i ) \u22121(x, Pi(x, s)) ) , (1.2) \u03c6i(x, |s|) \u2264 ai(x, s)s \u2264 Ai(x, s), (1.3) 2010 Mathematics Subject Classification. \u00d7 R+ \u2192 R+ with R \ufffd \u03c6max and a nonnegative function D \u2208 E\u03c6\u2217max (\u2126), such that for all s, t \u2208 R and for almost every x \u2208 \u2126, |\u03d5max(x, s)| \u2264 D(x) + (\u03c6\u2217max)\u22121(x,R(x, s)), (1.5) where \u03c6\u2217max stands for the complementary function of \u03c6max defined below in (2.1).", "mime": "application/pdf"}, {"id": "ejde-264", "words": "6555", "extension": ".pdf", "flesch": "82", "author": "Shan, Maria A.; Skrypnik, Igor I.; Voitovych, Mykhailo V.", "title": "Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth", "date": "2021", "keywords": "g(x; inequality", "summary": "Now, let \u03b41 \u2264 s < n/(n\u2212 1), and let j be a non-negative integer such that s (n\u2212 1 n )j+1 \u2264 \u03b41 \u2264 s (n\u2212 1 n )j . G(x0, u/\u03c1) \u03b6q dx \u2264", "mime": "application/pdf"}, {"id": "ejde-265", "words": "3986", "extension": ".pdf", "flesch": "83", "author": "Chernysh, Edward", "title": "Weakly monotone decreasing solutions to elliptic Schrodinger integral system", "date": "2021", "keywords": "u(x; |x|", "summary": "g(x) to state that there exists C,R > 0 such that f(x) \u2264 Cg(x) for all x satisfying |x| \u2265 R. Theorem 1.3. By (1.3), we may choose R > 0 such that min{\u03c6(x), \u03c8(x)} \u2265 \u03b30 > 0 whenever |x| \u2265 R\u2212 1.", "mime": "application/pdf"}, {"id": "ejde-268", "words": "8316", "extension": ".pdf", "flesch": "79", "author": "Li, Xiaoyan; Yang, Bian-Xia", "title": "Existence and multiplicity for radially symmetric solutions to Hamilton-Jacobi-Bellman equations", "date": "2021", "keywords": "problem; theorem", "summary": "Assuming (A5) we exclude the case when the projection of C onto the y-axis is a singleton, which is equivalent to C = {(a1, a2)}. Suppose that f satisfies (A1) and (A2). (a) If f0, f\u221e \u2208 (0,+\u221e) with f0 6= f\u221e, then for k \u2208 N, \u00b5 \u2208 (min{\u00b5 \u03bd k f0 , \u00b5\u03bdk f\u221e },max{\u00b5 \u03bd k f0 , \u00b5\u03bdk f\u221e }), problem (1.7) has at least one nodal solution u\u03bdk, such that \u03bdu\u03bdk has exactly k \u2212 1 simple zeros in (0, 1) and is positive near 0, where \u03bd \u2208 {+,\u2212}.", "mime": "application/pdf"}, {"id": "ejde-269", "words": "5110", "extension": ".pdf", "flesch": "84", "author": "Dix, Julio G.", "title": "Improved oscillation criteria for first-order delay differential equations with variable delay", "date": "2021", "keywords": "\u03c4(t", "summary": "= \u222b t t\u2217 p(s1) \u222b \u03c4(t) \u03c4(s1) p(s2) \u222b \u03c42(t) \u03c4(s2) p(s3)\u00b7 \u00b7 \u00b7 \u222b \u03c4n\u22121(t) \u03c4(sn\u22121) p(sn) dsn . . . For the basic step n = 2, we have\u222b t t\u2217 p(s1) \u222b \u03c4(t) \u03c4(s1) p(s2) ds2 ds1 \u2265 \u03c9 \u222b t t\u2217 p(s1) \u222b t s1 p(s2) ds2 ds1 = \u03c9 2! (\u222b t t\u2217 p(s) ds )2 , where the equality follows from Lemma 2.1.", "mime": "application/pdf"}, {"id": "ejde-27", "words": "9006", "extension": ".pdf", "flesch": "67", "author": "White, Luther W.; Malysheva, Tetyana; Karlstrom, Leif", "title": "Estimation of plate parameters from vertical displacement data using a family of plate models", "date": "2023", "keywords": "displacement; estimation; force; foundation; f\u0304v; mindlin; mindlin plate; models; parameters; plate; plate model; r3d", "summary": "The three plate models form a hierarchy of elastic plate models based on assumptions imposed on stresses, with the R3D plate model being the most generalized model and the thin plate model being the most constrained one. In fact, the problems of estimation of external forces and parameters for plate models have been of great practical interest in all fields of science and engineering where elastic plate models are employed.", "mime": "application/pdf"}, {"id": "ejde-270", "words": "6820", "extension": ".pdf", "flesch": "78", "author": "Ma, Li Ma; Yang, Guangzhengao", "title": "Hadamard type inequalities via fractional calculus in the space of exp-convex functions and applications", "date": "2021", "keywords": "convex; exp; function; hadamard; inequalities; type", "summary": "As a matter of fact, the development of mathematical inequalities is very closely related to the advances in the theory of convex function. As we know, the origin of the theory of convex function could be traced back to the literatures from many famous mathematicians, such as Jensen, Hardy, Hadamard.", "mime": "application/pdf"}, {"id": "ejde-271", "words": "3587", "extension": ".pdf", "flesch": "78", "author": "Liu, Zhenhai; Papageorgiou, Nikolaos S.", "title": "Dirichlet (p,q)-equations with gradient dependent and locally defined reaction", "date": "2021", "keywords": "1,p; papageorgiou", "summary": "Then we can find z0 \u2208 \u2126 such that u(z0) = max \u2126\u0304 u > M . For u \u2208 W 1,p 0 (\u2126) we define u\u00b1(z) = u(z)\u00b1 for all z \u2208 \u2126.", "mime": "application/pdf"}, {"id": "ejde-272", "words": "18300", "extension": ".pdf", "flesch": "82", "author": "Diz-Pita, Erika; Libre, Jaume; Otero-Espinar, M. Victoria", "title": "Phase portraits of a family of Kolmogorov systems depending on six parameters", "date": "2021", "keywords": "c0\u00b5; case; figure; node; phase; portrait; saddle; singular; stable", "summary": "We shall consider three cases: c0 < 0, c0 > 0, and c0 = 0. Conditions Classification 1.1 a0 > 0, c0 = 0, \u00b5 > 0, c2 < 0.", "mime": "application/pdf"}, {"id": "ejde-273", "words": "7965", "extension": ".pdf", "flesch": "80", "author": "Huu-Tai, Pierre Chau; Ducomet, Bernard", "title": "Energy-dependent Hamiltonian in a nuclear optical model", "date": "2021", "keywords": "dr\u2032", "summary": "Choosing R = R\u03b4 so large that for r > R, =m(\u03c1) \u2265 0 and |\u03c1| \u2265 \u03b4 one has |e(r, \u03c1)| > 1 2 e\u2212\u03c4r, \u03c4 = =m(\u03c1), we obtain \u222b \u221e R |e(r, \u03c1)|2dr \u2265 e\u2212\u03c4R 8\u03c4 , \u2016R(\u03bb)\u03a6R\u20162 \u2265 \u2016\u03a6R\u20162e\u2212\u03c4R |2e(\u03c1)| \u221a 2\u03c4 , which completes the proof. \u03c1 U(r\u2032, \u03c12)e(r\u2032, \u03c1) dr\u2032, (2.8) for \u03c1 6= 0 and =m(\u03c1) \u2265 0. (2) For any \u03b4 > 0 and for r \u2192\u221e e(r, \u03c1) = ei\u03c1r(1 + o(1)), \u2202re(r, \u03c1) = ei\u03c1r(i\u03c1+ o(1)), (2.9) uniformly with respect to \u03c1 in the domain {=m(\u03c1) \u2265 0, |\u03c1| > \u03b4}.", "mime": "application/pdf"}, {"id": "ejde-274", "words": "8223", "extension": ".pdf", "flesch": "79", "author": "Zeng, Shengda; Bai, Yunru; Gasinski, Leszek; Krech, Ireneusz", "title": "Existence of solutions for implicit obstacle problems involving nonhomogeneous partial differential operators and multivalued terms", "date": "2021", "keywords": "1,p; w 1,p", "summary": "\u03b7 \u2212 f, u\u3009 \u2265 a3 p\u2212 1 \u2016\u2207u\u2016pp \u2212 \u03b1j\u2016u\u2016pp \u2212 \u2016\u03b2j\u20161 \u2212 aK(w)\u2016u\u2016 \u2212 bK(w) \u2212 \u2016f\u2016W 1,p 0 (\u2126)\u2217\u2016u\u2016 \u2265 ( a3 p\u2212 1 \u2212 \u03b1j\u03bb\u22121 1,p)\u2016\u2207u\u2016pp \u2212 \u2016\u03b2j\u20161 \u2212 aK(w)\u2016u\u2016 \u2212 bK(w) \u2212 \u2016f\u2016W 1,p 0 (\u2126)\u2217\u2016u\u2016 \u2265 a3 p\u2212 1 \u2016u\u2016p \u2212 \u03b1jc(\u03b8)\u03b8\u2016u\u2016\u03b8 \u2212 \u2016\u03b2j\u20161 \u2212 aK(w)\u2016u\u2016 \u2212 bK(w)", "mime": "application/pdf"}, {"id": "ejde-275", "words": "6068", "extension": ".pdf", "flesch": "81", "author": "Donyari, Zahra; Zivari-Rezapour, Mohsen; Emamizadeh, Behrouz", "title": "Optimization problems and mathematical analysis of optimal values in Orlicz spaces", "date": "2021", "keywords": "lemma; uf\u0302", "summary": "We note that for f \u2208 A\u03b1, uf is positive, see [8, Lemma 3.4], and that uf \u2208W 2,\u03a6(\u2126), [3]. Let f \u2208 A\u03b1 and h \u2208 L\u221e(\u2126) be such that (i) \u222b \u21260 n h\u2212 dx = \u222b \u21261 n h+ dx for all n \u2208 N. (ii) limn\u2192\u221e \u2016\u03c7\u21260 n h\u2212\u2016\u221e", "mime": "application/pdf"}, {"id": "ejde-276", "words": "6829", "extension": ".pdf", "flesch": "84", "author": "Feng, Binhua; He, Zhiqian; Liu, Jiayin", "title": "Blow-up criteria and instability of standing waves for the inhomogeneous fractional Schrodinger equation", "date": "2021", "keywords": "blow; equation; schro\u0308dinger; u(t", "summary": "EJDE-2021/39 BLOW-UP CRITERIA FOR SCHRO\u0308DINGER EQUATIONS 17 References [1] T. Boulenger, D. Himmelsbach, E. Lenzmann; Blowup for fractional Schro\u0308dinger equation, J. Funct. [21] Y. Hong, Y. Sire; On fractional Schro\u0308dinger equations in Sobolev spaces, Comm.", "mime": "application/pdf"}, {"id": "ejde-277", "words": "7645", "extension": ".pdf", "flesch": "81", "author": "Urus, Nazia; Verma, Amit K.", "title": "Existence and uniqueness results for fourth-order four-point BVP arising in bridge design in the presence of reverse ordered upper and lower solutions", "date": "2023", "keywords": "bvp; linear; order; solution", "summary": "Step 5: Similarly, we deduce that u0 \u2264 \u00b7 \u00b7 \u00b7 \u2264 ln+1 \u2264 ln \u2264 \u00b7 \u00b7 \u00b7 \u2264 l1 \u2264 l0 = l(s). Thus we arrive at, the sequences ln and un such that u0 \u2264 u1 \u2264 \u00b7 \u00b7 \u00b7 \u2264 un \u2264 un+1 \u2264 \u00b7 \u00b7 \u00b7 \u2264 ln+1 \u2264 ln \u2264 \u00b7 \u00b7 \u00b7 \u2264 l1 \u2264 l0.", "mime": "application/pdf"}, {"id": "ejde-278", "words": "5658", "extension": ".pdf", "flesch": "77", "author": "Wang, Wei-Chuan", "title": "Existence of sign-changing solutions for radially symmetric p-Laplacian equations with various potentials", "date": "2021", "keywords": "laplacian; p\u22121; q\u2212p; solutions", "summary": "[23] B. Liu; Positive solutions of singular three-point boundary value problems for the one- dimensional p-Laplacian, Comput. [24] R. Ma; Positive solutions for multipoint boundary value problem with a one-dimensional p-Laplacian, Comput.", "mime": "application/pdf"}, {"id": "ejde-279", "words": "5616", "extension": ".pdf", "flesch": "76", "author": "Li, Xinyue; Zhang, Yongli; Zhang, Huiqun; Zhao, Qiulan", "title": "Lie symmetry analysis and conservation laws for the (2+1)-dimensional Mikhalev equation", "date": "2021", "keywords": "equation; mikhale\u0308v", "summary": "(3.31) Substituting (3.31) into (1.1), it is easily to obtain the reduced nonlinear PDE with variable coefficients through a straight calculation 2v3fv + v4fvv + c4vfvw \u2212 c4wfww \u2212 2v2ffv + wv2ffwv (3.27) 8 X. Y. LI, H. Q. ZHANG, Y. L. ZHANG, Q. L. ZHAO EJDE-2021/41 Solving this equation, we obtain v = (c3 \u2212 d3)y \u2212 d2x, w = t, u = d4 d2 y + f(w, v).", "mime": "application/pdf"}, {"id": "ejde-280", "words": "6146", "extension": ".pdf", "flesch": "83", "author": "Cai, Yuting; Wang, Chuncheng; Fan, Dejun", "title": "Stability and bifurcation in a delayed predator-prey model with Holling-type IV response function and age structure", "date": "2021", "keywords": "bifurcation; equation; predator; prey", "summary": "Let \u03c61(\u03c9) = arg{(Y \u2212 PN)\u03c92 +RH \u2212 Y Q+ (\u2212N\u03c92 + SH \u2212 PY +QN)i\u03c9}. = \u221a ((Y \u2212 PN)\u03c92 + (RH \u2212 Y Q))2 + ((SH \u2212 PY +QN)\u03c9 \u2212N\u03c93)2 \u00d7 sin(\u03c61(\u03c9)).", "mime": "application/pdf"}, {"id": "ejde-282", "words": "11196", "extension": ".pdf", "flesch": "83", "author": "Papanicolaou, Vassilis G.; Kallitsi, Eva; Smyrlis, George", "title": "Entire solutions for the heat equation", "date": "2021", "keywords": "equation; function; heat; order; sup", "summary": "(3.64) Then, from our assumption for the order and type of f(z), the integral in the right- hand side of (3.64) is entire in (t, z), satisfies the heat equation for every t, z \u2208 C (e.g., by analytic continuation) and it is clear from (3.64) that F (0, z) = f(z). Using (1.5) in (1.1) yields F (t0 + t, z0 + z) = \u2211 j,k\u22650 \u22022j+kz F (t0, z0) j!k! tjzk, t, z \u2208 C. (1.6)", "mime": "application/pdf"}, {"id": "ejde-283", "words": "7110", "extension": ".pdf", "flesch": "76", "author": "Long, Yuhua; Chen, Yining", "title": "Modeling porcine pseudorabies with age structure ", "date": "2021", "keywords": "disease; pseudorabies; system; \u2212n01", "summary": "Next, define a continuously differentiable function V : R5 + \u2192 R as V = \u03b1 \u03b21 (I1 \u2212 I\u22171 \u2212 I\u22171 ln I1 I\u22171 ) Owing to (2.1), there holds \u03b5 \u2264 min{\u03b1+ \u03b3, d2 \u2212 d1}, then detA \u2265d1(d1 + d2 + \u03be) (2\u03b1d2 + \u03b3(d1 + d2)\u2212 \u03b5(\u03b1+ d1 + d2))", "mime": "application/pdf"}, {"id": "ejde-284", "words": "8324", "extension": ".pdf", "flesch": "87", "author": "Wu, Yakui; Sun, Jiawei", "title": "Asymptotic behavior of linearized Boltzmann equations for soft potentials with cut-off", "date": "2021", "keywords": "lemma; operator", "summary": "We decompose (\u03bbI \u2212 B\u0302(\u03be))\u22121 as follows (\u03bbI \u2212 B\u0302(\u03be))\u22121 = (\u03bbI \u2212 B\u03020(\u03be))\u22121 + (\u03bbI \u2212 B\u03020(\u03be))\u22121(I \u2212 P (\u03bbI \u2212 B\u03020(\u03be))\u22121)\u22121P (\u03bbI \u2212 B\u03020(\u03be))\u22121. \u2229 %(A\u0302s(\u03be)), we have (\u03bbI \u2212 B\u03020(\u03be))\u22121 = (I \u2212 (\u03bbI \u2212 A\u0302s(\u03be))\u22121K0)\u22121(\u03bbI \u2212 A\u0302s(\u03be))\u22121.", "mime": "application/pdf"}, {"id": "ejde-285", "words": "8991", "extension": ".pdf", "flesch": "86", "author": "You, Song; Zhao, Peihao; Wang, Qingxuan", "title": "Existence and asymptotic behavior of positive least energy solutions for coupled nonlinear Choquard equations", "date": "2021", "keywords": "energy; solution; |x|\u03b1 \u2217", "summary": "Coupled Choquard equations; positive least energy solution; asymptotic behavior; variational method. This allows to consider positive least energy solution, which is defined as solution (u, v) of (1.4) with positive components and achieving the level inf{E(u, v) : E\u2032(u, v) = 0, (u, v) \u2208 H, u > 0 and v > 0}.", "mime": "application/pdf"}, {"id": "ejde-287", "words": "5440", "extension": ".pdf", "flesch": "77", "author": "Nunes, Ruikson S. O.", "title": "Exact boundary controllability for the wave equation with moving boundary domains in a star-shaped hole", "date": "2021", "keywords": "boundary; control; equation; wave", "summary": "Another interesting point it is to study on exact boundary control problems, in holed domains, for systems of coupled waves equations as proposed in [5, 16]. [4] W. D. Bastos, J. Ferreira; Exact boundary control for the wave equation in a polyhedral time-dependent domain, Appl Math Lett., 12 (1999), 1\u20135.", "mime": "application/pdf"}, {"id": "ejde-288", "words": "10368", "extension": ".pdf", "flesch": "75", "author": "Katarina S. Djordjevic, Katarina S.", "title": "Asymptotic formulas for q-regularly varying solutions of half-linear q-difference equations", "date": "2021", "keywords": "solution; varying", "summary": "This article studies the asymptotic behavior of positive solutions of the q-difference half-linear equation Dq(p(t)\u03a6(Dq(x(t)))) + r(t)\u03a6(x(qt)) (1.2) For recent papers investigating asymptotic behavior of positive solutions of (1.2) see [13, 14, 15].", "mime": "application/pdf"}, {"id": "ejde-289", "words": "5390", "extension": ".pdf", "flesch": "68", "author": "Bychkov, Evgeniy; Sviridyuk, Georgy; Bogomolov, Alexey", "title": "Optimal control for solutions to Sobolev stochastic equations", "date": "2021", "keywords": "control; equations; operator; problem; process; sobolev; space", "summary": "Optimal control problems for models of mathematical physics represent a promising direction We construct the noise space ClL2, l \u2208 N, as the space of random processes from CL2, whose trajectories are almost sure (a.s.)", "mime": "application/pdf"}, {"id": "ejde-290", "words": "10098", "extension": ".pdf", "flesch": "76", "author": "Alvarez-Caudevilla, Pablo; Colorado, Eduardo; Ortega, Alejandro", "title": "Existence of positive solutions for Brezis-Nirenberg type problems involving an inverse operator", "date": "2021", "keywords": "lemma; problem", "summary": "Introduction In this work, we analyze the existence of positive solutions of the second order elliptic equation under homogeneous Dirichlet boundary conditions and involving a non-local term, \u2212\u2206u = \u03b3(\u2212\u2206)\u22121u+ |u|p\u22121u in \u2126, u = 0 on \u2202\u2126, (1.1) where \u03b3 is a positive real parameter and \u2126 is a smooth bounded domain of RN , with N \u2265 3, 1 < p \u2264 2\u2217 \u2212 1, where 2\u2217 = 2N N\u22122 is the critical Sobolev exponent. Here, as customary (\u2212\u2206)\u22121u = v, if \u2212\u2206v = u in \u2126, v = 0 on \u2202\u2126. Thus, (\u2212\u2206)\u22121 is a positive linear integral compact operator from L2(\u2126) into itself, which is well-defined thanks to the Spectral Theorem.", "mime": "application/pdf"}, {"id": "ejde-291", "words": "5182", "extension": ".pdf", "flesch": "81", "author": "Carriao, Paulo Cesar; Costa, Augusto Cesar dos Reis; Miyagaki, Olimpio Hiroshi; Vicente, Andre", "title": "Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space", "date": "2022", "keywords": "0,r(\u03c9; kirchhoff", "summary": "We consider the functional J : H1 0,r(\u2126)\u2192 R associated with problem (2.1), J(v) = a 2 \u2016v\u20162 + b 4 \u2016v\u20164 \u2212 \u03bb q \u222b \u2126 p\u03b1|v|q \u2212 1 6 \u222b \u2126 |v|6, (2.2) whose Gateaux derivative is J \u2032(v)w = (a+ b\u2016v\u20162) \u222b \u2126 ( \u2207v \u00b7\u2207w+ 3 4 p2vw ) \u2212\u03bb \u222b \u2126 p\u03b1|v|q\u22122vw\u2212 \u222b \u2126 |v|4vw. From (2.13), we have d dt J(tv\u03b5)|t=t\u03b5 = 0, thus, at\u03b5\u2016v\u03b5\u20162 + bt3\u03b5\u2016v\u03b5\u20164 \u2212 \u03bbtq\u22121 \u03b5 \u222b \u2126 p\u03b1|v\u03b5|q \u2212 t5\u03b5 \u222b \u2126 |v\u03b5|6 = 0, EJDE-2021/53 KIRCHHOFF-TYPE PROBLEMS IN A HYPERBOLIC SPACE 7 which implies a\u2016v\u03b5\u20162 + bt2\u03b5\u2016v\u03b5\u20164 \u2212 \u03bbtq\u22122 \u03b5 \u222b \u2126 p\u03b1|v\u03b5|q \u2212 t4\u03b5 \u222b \u2126 |v\u03b5|6 = 0.", "mime": "application/pdf"}, {"id": "ejde-292", "words": "9017", "extension": ".pdf", "flesch": "85", "author": "Wang, Haoyu; Tian, Ge", "title": "Propagating interface in reaction-diffusion equations with distributed delay", "date": "2021", "keywords": "diffusion; equations; interface; proof", "summary": "ln \u03b5| \u21d2 1\u2212 \u03b5\u03c10 \u2264 u\u03b5(\u03b10\u03b5| ln \u03b5|+ \u03b5\u03c4 + \u03b5t, x) \u2264 1, t \u2208 There exists P > 1 such that, for sufficiently small \u03b5 > 0, it holds u\u2212\u03b7 (t, x) \u2264 u\u03b5(t+ \u03b10\u03b5| ln \u03b5|+ \u03b5\u03c4, x), \u2200 \u2212 \u03b5\u03c4 \u2264 t \u2264 0, x \u2208 RN , where \u03b10\u03b5| ln \u03b5| denotes the \u201cgeneration of interface from below time\u201d appearing in Proposition 2.11.", "mime": "application/pdf"}, {"id": "ejde-293", "words": "7487", "extension": ".pdf", "flesch": "72", "author": "Galiano, Gonzalo; Gonzalez-Tabernero, Victor", "title": "Turing instability analysis of a singular cross-diffusion problem", "date": "2021", "keywords": "b\u21920; cross; diffusion; instability; problem", "summary": "Then, for k \u2265 1 the linear problem to solve is: Find (un,k1 , un,k2 ) such that for for all \u03c7 \u2208 Sh 1 \u03c4 ( un,k1 \u2212 un\u22121 1 , \u03c7)h + ( d\u03b411(un,k\u22121)\u2202xu n,k 1 + d\u03b412(un,k\u22121)\u2202xu n,k 2 , \u2202x\u03c7 )h = ( un,k1 (\u03b1b1 \u2212 \u03b2b11u n,k\u22121 1 \u2212 \u03b2b12u n,k\u22121 2 ), \u03c7)h, 1 \u03c4 ( un,k2 \u2212 un\u22121 2 , \u03c7)h + ( d\u03b421(un,k\u22121)\u2202xu n,k 1 + d\u03b422(un,k\u22121)\u2202xu n,k 2 , \u2202x\u03c7 )h = ( un,k2 (\u03b1b2 \u2212 \u03b2b21u n,k\u22121 1 \u2212 \u03b2b22u n,k\u22121 2 )\u03c7)h. \u2212 k2 tr(D\u03b4(u\u2217))", "mime": "application/pdf"}, {"id": "ejde-294", "words": "8690", "extension": ".pdf", "flesch": "75", "author": "Montgomery-Smith, Stephen J.; Oveys, Hesam", "title": "Age-dependent branching processes and applications to the Luria-Delbruck experiment", "date": "2021", "keywords": "cell; daughter; function; generating; mother", "summary": "Cells have the following properties: (1) there are exactly two types of cells: mother cells and daughter cells; (2) all cells are independent of each other, mother cells are identical to other mother cells, and daughter cells are identical to other daughter cells; (3) cell life-span for mother cells and daughter cells are strictly positive, real- valued random variables Tx and Ty, respectively, with distributions P (t)", "mime": "application/pdf"}, {"id": "ejde-295", "words": "9407", "extension": ".pdf", "flesch": "83", "author": "Ochoa, Pablo; Ruiz, Julio Alejo", "title": "Solving singular evolution problems in sub-Riemannian groups via deterministic games", "date": "2021", "keywords": "carnot; equations; groups; p\u0302\u22121|g; \u00b5\u03b52", "summary": "\u03b5\u22121sj0\u3008\u03b7\u0302 \u2212 \u03b7, \u03bej0\u3009+ s20 2 E ( X\u0302 \u2212 X ) + s2j0 2 \u2329( X\u0302 \u2212 X ) \u03bej0 , \u03bej0 \u232a + [ F ( t, p, \u03b7, X\u0302 ) \u2212F ( t, p, \u03b7,X )] + [ F ( t, p, \u03b7\u0302, X\u0302 ) \u2212F ( t, p, \u03b7, X\u0302 )] . (5.10) 20 P. OCHOA, J. A. RUIZ EJDE-2021/57 If E(X\u0302 \u2212 X ) > 0, we chose |s0| = \u03bb1 with s0\u3008\u03b7\u0302 \u2212 \u03b7, \u03be0\u3009 \u2265 0. lim n\u2192\u221e sup q { ((u\u03b5)\u2217 \u2212 \u03d5)(tn \u2212 \u03b52, pn \u00b7 \u03b4\u03b5(q)) }", "mime": "application/pdf"}, {"id": "ejde-297", "words": "9545", "extension": ".pdf", "flesch": "73", "author": "Bunoiu, Renata; Karim, Karim; Timofte, Claudia", "title": "T-coercivity for the asymptotic analysis of scalar problems with sign-changing coefficients in thin periodic domains", "date": "2021", "keywords": "periodic; problem", "summary": "For u \u2208 H1(\u2126\u03b5), set T\u03b5u = { u1 in \u2126\u03b51, \u2212u2 + 2P\u03b5u1 in \u2126\u03b52. For u \u2208 H1(\u2126\u03b5), let T\u03b5u = { u1 \u2212 2Q\u03b5(u2 \u2212M\u03b5 2(u2)) in \u2126\u03b51, \u2212u2 + 2M\u03b5 2(u2) in \u2126\u03b52.", "mime": "application/pdf"}, {"id": "ejde-298", "words": "4396", "extension": ".pdf", "flesch": "77", "author": "Jesus, Isaias P. de; Cabanillas Lapa, Eugenio; Limaco, Juan", "title": "Controllability for the wave equation with moving boundary", "date": "2021", "keywords": "controllability; equation; wave; w\u03031; w\u03032", "summary": "Wave equation; Stackelberg-Nash strategies; controllability; inverse inequality. [2] A. Shao; On Carleman and observability estimates for wave equations on time-dependent domains, Proc.", "mime": "application/pdf"}, {"id": "ejde-299", "words": "7925", "extension": ".pdf", "flesch": "82", "author": "Chlebowicz, Agnieszka", "title": "Existence of solutions to infinite systems of nonlinear integral equations on the real half-axis", "date": "2021", "keywords": "equations; n=1; space", "summary": "\u2192 R+ which is nondecreasing on R+, con- tinuous at 0 and there exist a natural number p and a nonnegative integer q such that for any r > 0 and for x = (xi), y = (yi) \u2208 l1 with \u2016x\u2016l1 \u2264 r, \u2016y\u2016l1 \u2264 r and for t \u2208 R+, n \u2208 N, n \u2265 p+ 1 the following inequality |fn(t, x1, x2, . . .)| \u2264 l(r) n+q\u2211 i=n |xi \u2212 yi| holds for x = (xi), y = (yi) \u2208 l1 with \u2016x\u2016l1 \u2264 r, \u2016y\u2016l1 \u2264 r and for t \u2208 R+, 1 \u2264 n \u2264 p. (vii)", "mime": "application/pdf"}, {"id": "ejde-30", "words": "11980", "extension": ".pdf", "flesch": "84", "author": "Showalter, Ralph E.", "title": "Hilbert Space Methods for Partial Differential Equations", "date": "1994", "keywords": "linear; space; theorem", "summary": "A function T : V \u2192W is called conjugate linear if T (\u03b1x+ \u03b2y) = \u03b1\u0304T (x) + \u03b2\u0304T (y) , \u03b1, \u03b2 \u2208 K , x, y \u2208 V . A set K in the vector space V is convex if for x, y \u2208 K and 0 \u2264 \u03b1 \u2264 1, we have \u03b1x+(1\u2212\u03b1)y \u2208 K.", "mime": "application/pdf"}, {"id": "ejde-301", "words": "16403", "extension": ".pdf", "flesch": "79", "author": "Li, Mengyuan; Liu, Qihuai", "title": "Periodic orbits of the spatial anisotropic Kepler problem with anisotropic perturbations", "date": "2021", "keywords": "= \u2212; anisotropic; g \u221a; orbits; problem; \u2212 \u221a; \u221a \u22122h", "summary": "\u00d7 ( (1\u2212 p)(1\u2212G \u221a \u22122h)\u2212m )(1\u2212G \u221a \u22122h G \u221a \u22122h )m\u22121 and D2(G;h, p) = \u2212\u03b22p\u22121 \u221a \u22122h 2p\u22122 ( G \u221a \u22122h+ 1 )\u2212p\u22121 1\u2212p\u2211 m=0 Cm1\u2212p (1\u2212 p)! if |\u03b2| < 1/16, such that \u03b6\u03b5 \u00b1(0) tends to(1 2 , 1 2 cos g0 sin k0, 1 2 sin g0, \u221a 2 sin g0 cos k0, \u221a 2 sin g0 sin k0,\u2212 \u221a 2 cos g0 ) , as \u03b5\u2192 0 where g0 = \u00b11 2 arccos (\u221216\u03b2) .", "mime": "application/pdf"}, {"id": "ejde-302", "words": "6736", "extension": ".pdf", "flesch": "80", "author": "Idczak, Dariusz", "title": "Sensitivity of a nonlinear ordinary BVP with fractional Dirichlet-Laplace operator", "date": "2021", "keywords": "d((\u2212\u2206)\u03b2; function; j=1; x(t", "summary": "\u2208 L2. Assume that function f is measurable in t \u2208 (0, \u03c0), con- tinuously differentiable in (x, u) \u2208 Rm \u00d7 Rr and |f(t, x, u)|, |fx(t, x, u)|, |fu(t, x, u)| \u2264 a(t)\u03b3(|x|) + b(t)\u03b4(|u|) (5.1) for (t, x, u) \u2208 (0, \u03c0)\u00d7Rm \u00d7Rr, where a, b \u2208 L2 and \u03b3, \u03b4 : R+ 0 \u2192 R+ 0 are continuous functions.", "mime": "application/pdf"}, {"id": "ejde-303", "words": "14254", "extension": ".pdf", "flesch": "81", "author": "Pereira, Jardel Morais", "title": "Attractors for dissipative lattice differential equations with local and nonlocal nonlinearities", "date": "2021", "keywords": "attractors; i=1; lemma; n\u2208zd; proof; sup; t\u2264s\u2264t+1", "summary": "Since u = (un) and v = (vn) belong to `2, we have\u2211 n\u2208Zd (\u2206dun)vn = d\u2211 i=1 \u2211 n\u2208Zd (\u2202+i un)vn \u2212 d\u2211 i=1 \u2211 n\u2208Zd (\u2202\u2212i un)vn = d\u2211 i=1 \u2211 n\u2208Zd (\u2202+i un)vn \u2212 d\u2211 i=1 \u2211 n\u2208Zd (\u2202+i un)vn+ei = \u2212 \u2211 n\u2208Zd d\u2211 i=1 \u2202+i un\u2202 + i vn = \u2212 \u2211 n\u2208Zd \u2207+un \u00b7 \u2207+vn. This proves Lemma 2.2 if p = 1. \u2208 C1(R+; `2), from (3.34), we obtain (\u22121)2k+1 \u2211 n\u2208Zd \u22062k+1 d un(\u03b8nu\u0307n) = 1 2 d dt \u2211 n\u2208Zd \u03b8n|D2k\u22121vn|2 + \u2211 n\u2208Zd d\u2211 i=1 (\u2202+i \u03b8n)z (i) 2k\u22121,n + \u2211 n\u2208Zd d\u2211 i=1 \u2202+i \u03b8n [ (\u2202+i \u22062k d un)u\u0307n \u2212\u22062k d un(\u2202+i u\u0307n) ] , (3.35) where, in view of Lemma 2.1, \u2211 n\u2208Zd d\u2211 i=1 |z(i)2k\u22121,n| \u2264 C(2k \u2212 1, d)\u2016(v, v\u0307)\u20162H \u2264 16d2C(2k \u2212 1, d)\u2016(u, u\u0307)\u20162H , \u2211 n\u2208Zd d\u2211 i=1 |(\u2202+i \u22062k d un)u\u0307n \u2212\u22062k d un(\u2202+i u\u0307n)| \u2264 (4d)4k+1\u2016(u, u\u0307)\u20162H .", "mime": "application/pdf"}, {"id": "ejde-304", "words": "9198", "extension": ".pdf", "flesch": "82", "author": "Lin, Xiaolu; Zheng, Shenzhou", "title": "Multiplicity and asymptotic behavior of solutions to fractional (p,q)-Kirchhoff type problems with critical Sobolev-Hardy exponent", "date": "2021", "keywords": "lemma; p\u2217s(\u03b1; solutions", "summary": "\u3008I \u2032(un)\u2212 I \u2032(u), un \u2212 u\u3009 = m(\u2016un\u2016)\u3008un, un \u2212 u\u3009s,p \u2212m(\u2016un\u2016)\u3008u, un \u2212 u \u232a s,p + ( \u3008un, un \u2212 u\u3009s,q \u2212 \u3008u, un \u2212 u\u3009s,q ) + \u222b \u2126 ( |un|p \u2217 s(\u03b1)\u22122un \u2212 |u|p \u2217 s(\u03b1)\u22122u )( un \u2212 u ) |x|\u03b1 dx + \u03bb \u222b \u2126 f(x) ( |un|r\u22122un \u2212 |u|r\u22122u )( un \u2212 u ) |x|c dx. (3.15) (3.21) Let us now put (3.18), (3.19) and (3.21) into (3.15), which yields the inequality o(1) \u2265 m(\u2016un\u2016) ( \u3008un, un \u2212 u\u3009s,p \u2212 \u3008u, un \u2212 u\u3009s,p ) +m(\u2016un\u2016)\u3008u, un \u2212 u\u3009s,p \u2212m(\u2016un\u2016)\u3008u, un \u2212 u\u3009s,p. (3.22)", "mime": "application/pdf"}, {"id": "ejde-306", "words": "7500", "extension": ".pdf", "flesch": "92", "author": "Ali, Mageed; Iaia, Joseph", "title": "Infinitely many solutions for a singular semilinear problem on exterior domains", "date": "2021", "keywords": "r2\u2212n; va(ma; va(t", "summary": "Next integrating (2.15) on (t, R2\u2212N ) and dividing by (R2\u2212N \u2212 t) (2.27) Integrating on (t, R2\u2212N ) and using (2.3), (2.4) we obtain |Va(t)| = \u2223\u2223 \u222b R2\u2212N t V \u2032a(s) ds \u2223\u2223 \u2264 \u222b R2\u2212N t |V \u2032a(s)| ds \u2264 \u222b R2\u2212N t (aRN\u22121 N \u2212 2 + \u221a 2F0h(R2\u2212N ) ) ds = (R2\u2212N \u2212 t) (aRN\u22121 N \u2212 2 + \u221a 2F0h(R2\u2212N ) ) \u2264 aR N \u2212 2 +R2\u2212N \u221a 2F0h(R2\u2212N ).", "mime": "application/pdf"}, {"id": "ejde-307", "words": "22812", "extension": ".pdf", "flesch": "77", "author": "Llibre, Jaume; Oliveira, Regilene; Rodrigues, Camila A. B.", "title": "Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariantq", "date": "2021", "keywords": "case; darboux; eigenvalues; figure; invariant; line; phase; point; portraits; singular; system", "summary": "= y2 \u2212 x(x \u2212 1)(x \u2212 r) with r > 1 or f(x, y) = (x+ c)(\u03b12x+ \u03b32y + \u03b12), y\u0307 = \u2212(\u03b31/2)(x2 \u2212 y2 \u2212 1) + x(\u03b32x+ \u03b12y + c\u03b32), where \u03b12(c+ 1) = 0, (H.3) x\u0307", "mime": "application/pdf"}, {"id": "ejde-308", "words": "14933", "extension": ".pdf", "flesch": "76", "author": "Li, Shanbing; Xiao, Yanni; Dong, Yaying", "title": "Diffusive predator-prey models with fear effect in spatially heterogeneous environment", "date": "2021", "keywords": "fear; predator; prey; solution", "summary": "\u2212 d\u2212 audu,n \u2212 b(x)(v\u221e \u2212 \u03b5) ) udu,n , x \u2208 \u2126. A standard comparison argument yields udu,n \u2264 Udu,n in \u2126 for all large n, where Udu,n is the unique positive solution of \u2212du,n\u2206Udu,n = ( r 1 + k(v\u221e \u2212 \u03b5) It is clear that (1.4) admits a trivial solution (u, v) = (0, 0), two semi-trivial solutions (u, v) = ((r \u2212 d)/a, 0) with r > d and (u, v) = (0,m) with m > 0, and positive solutions (u, v) with no component identically zero.", "mime": "application/pdf"}, {"id": "ejde-309", "words": "4593", "extension": ".pdf", "flesch": "76", "author": "Chiyo, Yutaro; Mizukami, Masaaki", "title": "Existence of bounded global solutions for fully parabolic attraction-repulsion ", "date": "2021", "keywords": "system", "summary": "While finite-time blow-up was proved in the two-dimensional setting when \u03c7 > \u03be and the initial data satisfy the conditions that \u222b \u2126 u0 > 8\u03c0 \u03c7\u2212\u03be and that\u222b \u2126 u(x)|x\u2212 x0|2 dx (x0 \u2208 \u2126) is sufficiently small. [18] obtained global existence and boundedness when \u03c7 = 0 (or \u00b5 > \u03c7 \u2212 \u03be + M with some M > 0 in (1.1)).", "mime": "application/pdf"}, {"id": "ejde-310", "words": "5474", "extension": ".pdf", "flesch": "84", "author": "Cui, Pengxue; Ji, Shuguan", "title": "Existence and nonlinear stability of solitary wave solutions for coupled Schrodinger-KdV systems", "date": "2021", "keywords": "solitary; stability; wave", "summary": "\u2016q\u20162L2(R))\u03c6(\u03c6\u03d5)\u2032dx = 3\u2016\u03b31\u20162L(R) 1\u2212 c\u2212 4 3\u03b2(\u2212\u03c9 \u2212 c2 4 ) \u222b R \u03c63(x)\u03c6\u2032(x)dx = 0, (4.17) and (p\u22a5, \u03c6) = \u222b R p\u03c6+ 1 2 (\u2016p\u20162L2(R) + Schro\u0308dinger-KdV system; nonlinear stability; solitary wave solution.", "mime": "application/pdf"}, {"id": "ejde-312", "words": "6298", "extension": ".pdf", "flesch": "72", "author": "Koroleva, Yulia O.; Yu, Daria", "title": "Estimates of characteristics of a micropolar flow passing through an axially symmetric cell", "date": "2021", "keywords": "cell; curl; flow", "summary": "Micropolar fluid flow; porous medium; weak solution. = 1 N2 \u2206v1 + 2 curl\u03c91 \u2212 \u03b5\u03c32 N2 v1, L2\u2206\u03c91 + 1 2 N2 1\u2212N2 curl v1 \u2212 N2 1\u2212N2 \u03c91 = 0. (2.14) div v2 = 0,( 1 N2 \u2212 1 ) \u2207p2 = 1 N2 \u2206v2 + 2 curl\u03c92, L2\u2206\u03c92 + 1 2 N2 1\u2212N2 curl v2 \u2212 N2 1\u2212N2 \u03c92 = 0. (2.15)", "mime": "application/pdf"}, {"id": "ejde-313", "words": "10494", "extension": ".pdf", "flesch": "87", "author": "Jleli, Mohamed; Samet, Bessem", "title": "Nonexistence results for hyperbolic type inequalities involving the Grushin operator in exterior domains", "date": "2021", "keywords": "g(y)d\u03c3y; p\u22121; \u2202d1; \u2202d2", "summary": "\u22121 p\u22121 dx ) \u2264 C ( R \u22122\u03b8p p\u22121 R2\u03b8 lnR+R \u2212\u03b8p p\u22121R\u03b8 ( p\u22122 p\u22121 ) (lnR) \u22121 p\u22121 ) \u2264 CR \u22122\u03b8 p\u22121 lnR. 12 M. JLELI, B. SAMET EJDE-2021/75 For N1 \u2265 3 and R\u03b8 < |x| < 2R\u03b8, proceeding as above, and using Lemma 3.3, we obtain b \u22121 p\u22121 |\u2206xb| p p\u22121 \u2264 C ( R \u22122\u03b8p p\u22121 ( 1\u2212 |x|2\u2212N1 ) Hence, for 1 < p < N1 N1\u22122 , taking 0 < 2\u03c3 < 2p p\u22121 \u2212 N1 and passing to the limit as R \u2192 \u221e in the above inequality, we obtain a contradiction with \u222b \u2202D1 g(y)d\u03c3y > 0.", "mime": "application/pdf"}, {"id": "ejde-314", "words": "9340", "extension": ".pdf", "flesch": "87", "author": "Drabek, Pavel; Zahradnikova, Michaela", "title": "Traveling waves for unbalanced bistable equations with density dependent diffusion", "date": "2021", "keywords": "p\u22121", "summary": "Preliminaries Let g : [0, 1]\u2192 R, g \u2208 C[0, 1] be such that g(0) = g(s\u2217) = g(1) = 0 for s\u2217 \u2208 (0, 1) and g(s) \u2264 0, s \u2208 (0, s\u2217), g(s) > 0, s \u2208 (s\u2217, 1). Note that f \u2208 L1(0, 1) implies that h = h(t, y, c) satisfies Carathe\u0301odory\u2019s conditions, i.e., for a.e. t \u2208", "mime": "application/pdf"}, {"id": "ejde-315", "words": "5311", "extension": ".pdf", "flesch": "86", "author": "Wan, Youyan; Tan, Jinggang", "title": "Standing waves to Chern-Simons-Schrodinger systems with critical exponential growth", "date": "2021", "keywords": "chern; schro\u0308dinger", "summary": "4 Y. WAN, J. TAN EJDE-2021/77 Again we can derive from \u22021A2 \u2212 \u22022A1 = \u2212 1 2u 2 that\u222b R2 A0|u|2 In fact, since \u2016un\u2016 \u2264 c0, J(un)\u2192 c, and J \u2032(un)\u2192 0, we have\u222b R2 F (un) = 1 2 \u2016un\u20162 + 1 2 \u222b R2 ( A2 1,n|un|2 +A2 2,n|un|2 ) dx\u2212 c+ on(1),\u222b R2 f(un)un dx = \u2016un\u20162 + 3 \u222b R2 ( A2 1,n +A2 2,n ) u2 n dx\u2212 \u03b5n\u2016un\u2016, where \u03b5n \u2192 0 as n\u2192\u221e. By Proposition 2.1 and Sobolev embedding theorem, we obtain \u222b R2 F (un) \u2264 1 2 \u2016un\u20162 + C\u2016un\u20164 \u2212 c+ on(1),\u222b R2 f(un)un dx = \u2016un\u20162 + C\u2016un\u20164 \u2212 \u03b5n\u2016un\u2016. From \u2016un\u2016 \u2264 c0, we obtain \u222b R2 f(un)un dx \u2264 c0 and \u222b R2 F (un) dx \u2264 c0.", "mime": "application/pdf"}, {"id": "ejde-316", "words": "5499", "extension": ".pdf", "flesch": "82", "author": "Ishibashi, Kazuki", "title": "Hille-Nehari type non-oscillation criteria for half-linear dynamic equations with mixed derivatives on a time scale", "date": "2021", "keywords": "non; theorem", "summary": "Half-linear dynamic equations; nonoscillation; time scale; Riccati dynamic inequality; linear differential equation; linear difference equation. Let T = R and p = 2.", "mime": "application/pdf"}, {"id": "ejde-317", "words": "7277", "extension": ".pdf", "flesch": "82", "author": "Guo, Ying-Jia; Jiang, Xiao-Meng", "title": "Stochastic Newtonian equations with mean boundary conditions", "date": "2021", "keywords": "boundary; conditions; equations; f(u; \u222b b; \u222b t", "summary": "= \u222b t a Y (s)ds =\u2212 t\u2212 a b\u2212 a \u222b b a ds \u222b s a E[f(u, x\u0304(u) + y(u))\u2212 f(u, x\u0304(u))]du + \u222b t a ds \u222b s (3.31) Combining (3.29), (3.30) and (3.31), we conclude that for all t \u2208 [a, b], y(t) = \u2212 t\u2212 a b\u2212 a \u222b b a ds \u222b s a E[f(u, x\u0304(u) + y(u))\u2212 f(u, x\u0304(u))]du + \u222b t a ds \u222b s a [f(u, x\u0304(u) + y(u))\u2212 f(u, x\u0304(u))]du + \u222b t a ds \u222b s a g(u, x\u0304(u) + y(u))dB(u)", "mime": "application/pdf"}, {"id": "ejde-318", "words": "10145", "extension": ".pdf", "flesch": "82", "author": "Webb, Jeffrey R. L.", "title": "A fractional Gronwall inequality and the asymptotic behaviour of global solutions of Caputo fractional problems", "date": "2021", "keywords": "fractional; u(t", "summary": "Suppose that u \u2208 C+[0, T ] satisfies u(t) \u2264 a(t) + \u222b t 0 \u03c6(s)u(s) ds for t \u2208 If x \u2208 L\u221e+ [0, T ] satisfies the inequality x(t) \u2264 a(t) + g(t) \u222b t 0 (t\u2212 s)\u03b2\u22121x(s)ds, t \u2208", "mime": "application/pdf"}, {"id": "ejde-32", "words": "3339", "extension": ".pdf", "flesch": "64", "author": "Feng, Zaichun (Z.C.); Li, Y. Charles", "title": "Enrichment paradox and applications", "date": "2023", "keywords": "predator; prey", "summary": "Dynamics of (2.1)-(2.2) when r = 1/2, k = 1, H = 1.69, \u03bd = 2. such as plagues also caused human population to temporarily decrease. But since 1700, human population has been monotonically increasing due to technological advances.", "mime": "application/pdf"}, {"id": "ejde-320", "words": "7614", "extension": ".pdf", "flesch": "76", "author": "Hafeez, Usman; Lavier, Theo; Williams, Lucas; Korobenko, Lyudmila", "title": "Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators", "date": "2021", "keywords": "inequality; orlicz; sobolev", "summary": "Let u be a weak solution to (1.1) on \u2126 = B and define u+ = max{u, 0}, then the following Caccioppoli inequality holds on the ball B\u222b {x\u2208B:u(x)>0} |\u2207Au+|2 d\u00b5 \u2264 \u222b {x\u2208B:u(x)>0} u+\u2016f\u2016L\u221e d\u00b5, where d\u00b5 = dx|B|. Proof. Moreover, if the above estimate holds for q = \u03c3\u2032 then Sobolev inequality (1.2) holds (almost necessity).", "mime": "application/pdf"}, {"id": "ejde-321", "words": "53541", "extension": ".pdf", "flesch": "81", "author": "Bujac, Cristina; Schlomiuk, Dana; Vulpe, Nicolae", "title": "Cubic differential systems with invariant straight lines of total multiplicity seven and four real distinct infinite singularities", "date": "2021", "keywords": "= 0; = \u2212; bujac; case; complex; condition; configurations; direction y; ejde-2021/; family; g \u2212; invariant; lemma; lines; multiplicity; p =; p+ r; parameter; point; possibility; r \u2212; r)(1; real; schlomiuk; singularities; system; total; transformation; u 6=; u =; vulpe", "summary": "= 2\u221243\u22129(X \u2212 2Y )(3X \u2212 4mZ)3(3X \u2212 3Y \u2212 2mZ)2(3Y \u2212 2mZ)2 and hence by Lemma 2.6 we have invariant lines of total multiplicity nine, i.e. we are not in the class of systems with invariant lines of total multiplicity exactly seven. 1.2.2. So considering these conditions as well as the conditions (3.145) and (3.146) we calculate H2 = 8r(1 + r)(2 + 2r + u)3 (1 + u)3(r + u)3\u2206cf V1V2V3, H \u20322 = \u22128r6(1 + r)(1 + r \u2212 u)3 (1 + u)3(r + u)3\u2206cf V1V2V4, where V1 = h(2r \u2212 u)(r + u) +m(u\u2212 2)(1 + u), V2 = hr(r + u)(3 + r + u) +m(1 + u)(1 + 3r + u), V3 = hr(r + u)(2r + 4r2 + 2r3 \u2212 u+ 2ru+ 3r2u\u2212 8u2 + 2r2u2 \u2212 4u3 + 3ru3 + u4) +m(1 + u)(r3u\u2212 2r \u2212 4r2 \u2212 2r3 \u2212 3ru\u2212 2r2u\u2212 2u2 + 8r2u2 \u2212 3u3 + 4ru3 \u2212 u4), V4 = h(r + u)(2r3 + 2r4 \u2212 2r \u2212 2r2 + u\u2212 7ru\u2212 9r2u\u2212 r3u+ u2 \u2212 15ru2 \u2212 10r2u2 \u2212 u3 \u2212 8ru3 \u2212 u4) +m(1 + u)(2 + 2r \u2212 2r2 \u2212 2r3 \u2212 u\u2212 9ru\u2212 7r2u+ r3u\u2212 10u2 \u2212 15ru2 + r2u2 \u2212 8u3 \u2212 ru3 \u2212 u4).", "mime": "application/pdf"}, {"id": "ejde-322", "words": "6660", "extension": ".pdf", "flesch": "80", "author": "Antontsev, Stanislav; Ferreira, Jorge; Piskin, Erhan; Yuksekkaya, Hazal; Shahrouzi, Mohammad", "title": "Blow up and asymptotic behavior of solutions for a p(x)-Laplacian equation with delay term and variable exponents", "date": "2021", "keywords": "er(t; m(x; \u222b t; \u222b \u03c9", "summary": "= (1\u2212 \u03b1)H\u2212\u03b1(t)H \u2032(t) + \u03b5 \u222b \u2126 u2 tdx\u2212 \u03b5 \u222b \u2126 |\u2207u|p(x)dx + \u03b5b \u222b \u2126 |u|q(x)dx\u2212 \u03b5\u00b51 \u222b \u2126 uut(x, t)|ut(x, t)| m(x)\u22122 dx \u2212 \u03b5\u00b52 \u222b \u2126 uz(x, 1, t)|z(x, 1, t)| m(x)\u22122 dx. dx d\u03c1 EJDE-2021/84 BLOW UP AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS 9 + \u03b5 \u222b \u2126 u2 tdx\u2212 \u03b5 \u222b \u2126 |\u2207u|p(x) + \u03b5ab \u222b \u2126 |u|q(x)dx \u2212 \u03b5\u00b51 \u222b \u2126 uut(x, t)|ut(x, t)| m(x)\u22122 dx \u2212 \u03b5\u00b52 \u222b \u2126 uz(x, 1, t)|z(x, 1, t)| m(x)\u22122 dx.", "mime": "application/pdf"}, {"id": "ejde-323", "words": "4764", "extension": ".pdf", "flesch": "73", "author": "Feng, Sebert", "title": "Symmetry analysis for a second-order ordinary differential equation", "date": "2021", "keywords": "differential; equation; lie; symmetry", "summary": "Hence, the general solution of the linearized symmetry condition is \u03be = \u2212 (q + 2)c0 k2 e k2q q+2x + c1, \u03b7 = c0e k2q q+2xy. (4.5) Substituting (4.5) into (4.2), we have \u03b7 = \u2212 2a(x)k1 (q + 1)(q + 2) yq+2 + {a\u2032(x)\u2212 a(x)k2}y2 + c(x)y + d(x), (4.6) where q 6= \u22121 and q 6= \u22122.", "mime": "application/pdf"}, {"id": "ejde-324", "words": "7300", "extension": ".pdf", "flesch": "80", "author": "Li, Mengni", "title": "Singular Monge-Ampere equations over convex domains", "date": "2021", "keywords": "convex; domain; n+\u03b1; solution", "summary": "By constructing a family of sub-solutions, we prove the existence and global Ho\u0308lder estimates of convex solutions to the problem over convex domains. For any point y \u2208 \u2126, we can find z \u2208 \u2202\u2126 be the nearest boundary point to y. Without loss of generality, we assume that the domain \u2126 satisfies the exterior sphere condition with radius R. By some translations and rotations, we can further assume z = 0, 0 \u2208 \u2202\u2126 \u2229 \u2202BR(y0), \u2126 \u2282 BR(y0), and the line yz is the xn-axis.", "mime": "application/pdf"}, {"id": "ejde-326", "words": "5166", "extension": ".pdf", "flesch": "64", "author": "Fama, Alessio; Restuccia, Liliana", "title": "Coupled porosity-fluid concentration flux-temperature waves in isotropic porous media", "date": "2021", "keywords": "equation; fluid; flux; ijkl; propagation", "summary": "j c \u2202jci \u2202t = \u2212jci + (3\u03be3 1 + 2\u03be3 2)r,i + \u03be5T,i, (6.2) i.e. equation (3.14), when we define \u03b2c = \u03be5, \u03b1c = 3\u03be3 1 + 2\u03be3 2 . (6.3) 7. Appendix D: Derivation of temperature equation To deduce (3.15), we use (3.3) , (3.11), (3.12)1, and (3.12)5, and the special forms (3.8)2, (3.8)3 , and (4.5) of the tensors Kij , \u03b7ij and \u03bd3 ijkl, so that we obtain \u03c4 q \u22022T \u2202t2 + \u2202T \u2202t = 3\u03b7 \u2202r \u2202t +KT,ii +D\u03bd [ \u03bd3 1\u03b4il\u03b4jk + \u03bd3 2(\u03b4ij\u03b4kl + \u03b4ik\u03b4jl) ] r,li\u03b4jk, (7.1) where \u03bd3 1 , \u03bd3 2 are the 2 significant independent components of the fourth tensor \u03bd3 ijkl and K, \u03b7 are the only significant components of the second order tensors Kij and \u03b7ij . In [25, 26] the constitutive equations and rate equations were obtained (to close the systems of balance equations, see [25]) obeying the objectivity and frame indifference principles", "mime": "application/pdf"}, {"id": "ejde-327", "words": "3420", "extension": ".pdf", "flesch": "82", "author": "Dao, Nguyen Anh; Diaz, Jesus Ildefonso", "title": "Logarithmically improved regularity criteria for the Navier-Stokes equations in homogeneous Besov spaces", "date": "2021", "keywords": "regularity", "summary": "To be more precise, if\u222b T 0 \u2016w(\u03c4)\u2016L\u221e d\u03c4 <\u221e , then the smooth solution u, in C([0, T );W s,p(Rn)), with s > n/p + 1, can be continued beyond t = T . Thanks to the Gagliardo\u2013Nirenberg inequality, we obtain \u2016(\u2212\u2206) s0 2 u(t)\u2016L2 \u2264 \u2016u(t)\u20161\u2212 s0 s L2 \u2016(\u2212\u2206)s/2u(t)\u2016 s0 s L2 \u2264 \u2016u\u2016 1\u2212 s0s L\u221e(0,T ;L2)\u2016(\u2212\u2206)s/2u(t)\u2016 s0 s L2 for t \u2208 (0, T ).", "mime": "application/pdf"}, {"id": "ejde-328", "words": "5540", "extension": ".pdf", "flesch": "82", "author": "Aguilera Contreras, Gabriel; Munoz-Rivera, Jaime E.", "title": "Bresse systems with localized Kelvin-Voigt dissipation", "date": "2021", "keywords": "beam", "summary": "More precisely, we consider the system \u03c11\u03d5tt \u2212 Sx \u2212 lN = 0 in I\u0303 \u00d7 (0,+\u221e), (1.1) \u2212\u2212lK(zx \u2212 lv)x \u2212 lK(zxt \u2212 lvt)x + l\u03ba(vx + y + lz) + l\u03ba\u0303(vxt + yt + lzt) = 0. (4.5) EJDE-2021/90 BRESSE SYSTEMS 13 Multiplying (4.3) by vt, and (4.4) by wt, and integrating on [0, `], we obtain\u222b ` 0 ( \u03c11|vt|2 + \u03c12|yt|2 + \u03c11|zt|2 + b|yx|2 + \u03ba|vx + y + lz|2 +K|zx \u2212 lv|2 )", "mime": "application/pdf"}, {"id": "ejde-329", "words": "11145", "extension": ".pdf", "flesch": "86", "author": "Messaoudi, Salim A.; Bouhoufani, Oulia; Hamchi, Ilhem; Alahyane, Mohamed", "title": "Existence and blow up in a system of wave equations with nonstandard nonlinearities", "date": "2021", "keywords": "blow; existence; p\u2212+1; \u03c1(v", "summary": ", \u03c9k}, as follows uk(x, t) = \u03a3kj=1aj(t)\u03c9j(x), vk(t) = \u03a3kj=1bj(t)\u03c9j(x), for x \u2208 \u2126 and t \u2208 (0, T ), satisfying the approximate problems\u222b \u2126 uktt(x, t)\u03c9jdx+ \u222b \u2126 A\u2207uk(x, t) \u00b7 \u2207\u03c9jdx + \u222b \u2126 |ukt (x, t)|m(x)\u22122ukt (x, t)\u03c9jdx = \u222b \u2126 f(x, t)\u03c9jdx,\u222b \u2126 vktt(x, t)\u03c9jdx+ \u222b \u2126 B\u2207vk(x, t) \u00b7 \u2207\u03c9jdx + \u222b \u2126 |vkt (x, t)|r(x)\u22122vkt (x, t)\u03c9jdx = \u222b \u2126 g(x, t)\u03c9jdx, (3.5) for j Introduction In this work, we study the following initial-boundary-value problem for the un- knowns u and v: utt \u2212 div(A\u2207u) + |ut|m(x)\u22122ut = f1(x, u, v) in \u2126\u00d7 (0, T ), vtt \u2212 div(B\u2207v) + |vt|r(x)\u22122vt = f2(x, u, v) in \u2126\u00d7 (0, T ), u = v = 0 on \u2202\u2126\u00d7 (0, T ), u(0) = u0, ut(0) = u1 in \u2126, v(0)", "mime": "application/pdf"}, {"id": "ejde-33", "words": "8349", "extension": ".pdf", "flesch": "83", "author": "Allal, Brahim; Fragnelli, Genni; Salhi, Jawad", "title": "Null controllability of coupled systems of degenerate parabolic integro-differential equations", "date": "2023", "keywords": "controllability; dt dx", "summary": "= 0, t \u2208 (0, T ),{ y1(t, 0) = y2(t, 0) = 0, if a is strongly degenerate, t \u2208 (0, T ), y1(0, x) = y0 1(x), y2(0, x) = y0 2(x), x \u2208 (0, 1), (1.1) where Q = (0, T )\u00d7(0, 1), \u03c9 b (0, 1) is a non-empty open set, 1\u03c9 is the corresponding characteristic function, bij := bij(t, x) \u2208 L\u221e(Q) and u = u(t, x) is the distributed control function.", "mime": "application/pdf"}, {"id": "ejde-330", "words": "7903", "extension": ".pdf", "flesch": "88", "author": "Bellaama, Rachid; Belaidi, Benharrat", "title": "Lower order for meromorphic solutions to linear delay-differential equations", "date": "2021", "keywords": "f(z; \u00b5(al0", "summary": "(3.29) We may choose \u03b5 sufficiently small satisfying 0 < 3\u03b5 < min { \u00b5(Al0)\u2212 \u03c1, \u00b5(Al0)\u2212 \u03bb ( 1 Al0 )} , it follows from (3.29) that for r \u2208 E6 \\ E8, r \u2192 +\u221e, r\u00b5(Al0)\u22122\u03b5 \u2264 r\u03c1(f)+\u03b5, this means, \u00b5(Al0) \u2264 \u03c1(f) + (3.30) We choose \u03b5 sufficiently small satisfying 0 < 3\u03b5 < min { \u00b5(Al0)\u2212 \u03c1, \u00b5(Al0)\u2212 \u03bb( 1 Al0 ) } , from (3.30) that for r \u2208 E6 \\ E8, r \u2192 +\u221e, r\u00b5(Al0)\u22122\u03b5 \u2264 r\u03c1(f)\u22121+\u03b5, this means, \u00b5(Al0) \u2264 \u03c1(f)\u22121 + 3\u03b5, since \u03b5 > 0 is arbitrary, then \u03c1(f) \u2265 \u00b5(Al0) + 1. 12 R. BELLAAMA, B. BELAI\u0308DI EJDE-2021/92 Case 2: \u03b2 = \u03c1(S) < \u00b5(Al0)", "mime": "application/pdf"}, {"id": "ejde-331", "words": "5986", "extension": ".pdf", "flesch": "83", "author": "Wang, Lianwen; Mubarak, Abdulrahman", "title": "Monotone solutions of first order nonlinear differential systems", "date": "2021", "keywords": "solutions; theorem", "summary": "Indeed, if limt\u2192\u03b1\u2212 x(t) < \u221e, it follows from y(t) = y(a) + \u222b t a q(s)g(x(s))ds that lim t\u2192\u03b1\u2212 y(t) = y(a) + \u222b \u03b1 a q(t)g(x(t))dt <\u221e. So (x, y) can be extended to [a, \u03b1] and further to a small neighborhood at the right of \u03b1. By (H2) both f(x(t)) and g(y(t)) are increasing on [c, \u03b1), then y(t) = y(c) + \u222b t c q(s)g(x(s))ds \u2264 y(c) + g(x(t)) \u222b t c q(s)ds = g(x(t)) ( y(c) g(x(t)) + \u222b t c q(s)ds ) \u2264 g(x(t)) ( y(c) g(x(c))", "mime": "application/pdf"}, {"id": "ejde-332", "words": "7942", "extension": ".pdf", "flesch": "91", "author": "Ding, Yuanlin; Wang, Jinrong", "title": "Periodic solutions for conformable type non-instantaneous impulsive differential equations", "date": "2021", "keywords": "n(a", "summary": "= Qz(\u03b9\u2212k ), \u03b9 \u2208 (\u03b9k, \u03c3k], k = 1, 2, . . = za \u2208 Rn, (1.2) and the conformable nonlinear non-instantaneous impulsive differential equation D\u03c3k \u03b2 z(\u03b9) = Pz(\u03b9) + h(t, z(\u03b9)), \u03b9 \u2208 (\u03c3k, \u03b9k+1], k = 0, 1, 2, . . .", "mime": "application/pdf"}, {"id": "ejde-333", "words": "8566", "extension": ".pdf", "flesch": "82", "author": "Liu, Zhiqing; Gao, Cunchen; Fang, Zhong Bo", "title": "Well-posedness and energy decay of a transmission problem of Kirchhoff type wave equations with damping and delay terms", "date": "2021", "keywords": "problem; \u2016\u2207u\u20162\u03c91", "summary": "Substituting (3.19)-(3.22) into (3.17), we can derive d dt E (n) 1 (t) + r(1\u2212 3\u03b7)\u2016u(n) tt \u20162\u03932 \u2264 3\u2016\u2207u(n)\u2016\u21261\u2016\u2207u (n) t \u20163\u21261 + 3\u2016\u2207v(n)\u2016\u21262\u2016\u2207v (n) t \u20163\u21262 \u2212 (\u00b51 \u2212 \u00b52 2 \u2212 \u03b6 2\u03c4 )\u2016u(n) tt \u20162\u21261 \u2212 ( \u03b6 2\u03c4 \u2212 \u00b52 2 )\u2016z(n) t (x, 1, t)\u20162\u21261 + r 4\u03b7 (k\u2032(t))2\u2016k\u2032\u2032(t\u2212 s)\u2016L1(0,+\u221e) \u222b t 0 k\u2032\u2032(t\u2212 A direct calculation shows that (h \u2217 u, ut)\u03932 =\u2212 1 2 d dt [ \u222b \u03932 (h \ufffd u)(t)d\u0393\u2212 (\u222b t 0 h(s)ds ) \u2016u\u20162\u03932 ] \u2212 1 2 h(t)\u2016u\u20162\u03932 + 1 2 \u222b \u03932 (h\u2032 \ufffd u)(t)d\u0393, (2.1) and \u2016(h \u25e6 u)(t)\u20162\u03932 \u2264 (\u222b t 0 |h(s)|ds )\u222b \u03932 (|h| \ufffd u)(t)d\u0393. (2.2) Differentiating (1.3), we arrive at the following Volterra equation (1 + \u2016\u2207u\u20162\u21261 )", "mime": "application/pdf"}, {"id": "ejde-334", "words": "7208", "extension": ".pdf", "flesch": "81", "author": "hao, Xutong; Zhou, Mingjun; Jing, Xinxin", "title": "Asymptotic behavior of solutions to porous medium equations with boundary degeneracy", "date": "2021", "keywords": "problem", "summary": "= \u222b 1 0 u(x, t)\u03b7\u03b4(x)dx, t \u2265 0. = \u222b 1 0 u(x, t)\u03b7(x)dx, t \u2265 0.", "mime": "application/pdf"}, {"id": "ejde-335", "words": "6876", "extension": ".pdf", "flesch": "76", "author": "Neto, Antonio Francisco", "title": "Extending Putzer's representation to all analytic matrix functions via omega matrix calculus", "date": "2021", "keywords": "calculus; d\u22121\u2211; fractional; k=0; lemma; matrix; theorem", "summary": "exp(tA)\u03c60, where the matrix exponential exp(A) is defined by exp(A) = \u2211 k\u22650 Ak/k!, (1.2) which is a matrix valued convergent power series for any A \u2208 CN\u00d7N . = 1 \u0393(\u03b1) \u222b t 0 (t\u2212 s)\u03b1\u22121f(s)ds, t > 0, where \u0393(\u03b1) is the Euler\u2019s gamma function", "mime": "application/pdf"}, {"id": "ejde-336", "words": "5975", "extension": ".pdf", "flesch": "83", "author": "aguchi, Dai; Tsuchiya, Takahiro", "title": "Newton-Kantorovitch method for decoupled forward-backward stochastic differential equations", "date": "2021", "keywords": "t t", "summary": "[0, T ]\u2192 Rm\u00d7k adapted : \u2016Z\u2016H2 <\u221e}, where the norms \u2016 \u00b7 \u2016L2 T , \u2016 \u00b7 \u2016S2m , and \u2016 \u00b7 \u2016H2 are defined by \u2016Y \u2016L2 T = \u2016Y \u2016S2m = {E[ sup 0\u2264s\u2264T |Y (s)|2]}1/2, \u2016Z\u2016H2 = {E[ \u222b T 0 |Z(s)|2 ds]}1/2. For \u03b1 \u2208 R, we introduce the weighted norm \u2016(Y,Z)\u20162\u03b1 = E[ sup 0\u2264s\u2264T e\u03b1s|Y (s)|2] + E[ \u222b T 0 e\u03b1s|Z(s)|2 ds].", "mime": "application/pdf"}, {"id": "ejde-337", "words": "4710", "extension": ".pdf", "flesch": "84", "author": "Bieske, Thomas; Blackwell, Keller", "title": "Generalizations of the drift Laplace equation in the Heisenberg group and Grushin-type spaces", "date": "2021", "keywords": "equation; group; theorem", "summary": "We begin with R3 using the coordinates (x1, x2, x3) and consider the linearly independent vector fields {X1, X2, X3}, defined by: X1 = \u2202 \u2202x1 \u2212 x2 2 \u2202 \u2202x3 , X2 = \u2202 \u2202x2 + x1 2 \u2202 \u2202x3 , X3 = \u2202 \u2202x3 which obey the relation [X1, X2] = X3. \u2212 a)3n(y2 \u2212 b) (\u03b1+ \u03b2 \u2212 1)g\u03b1+\u03b2\u22122h\u03b1+\u03b2\u22122 (4.7) and 2\u2211 i=1 Yi\u2016\u22070f\u20162(Yif) = 4c3(n+ 1)3(\u03b12 + \u03b22)(y1 \u2212 a)3n\u22121g2\u03b1+\u03b2\u22123h\u03b1+2\u03b2\u22123 \u00d7 ( (\u03b1h+ \u03b2g) ( ngh+ c2(n+ 1)(\u03b1+ \u03b2 \u2212 1)(y1 \u2212 a)2n+2 ) + ic(n+ 1)2(y1 \u2212 a)n+1(y2 \u2212 b)(\u03b1+ \u03b2 \u2212 1)(\u03b1h\u2212 \u03b2g) ) , \u2016\u22070f\u20162(Y1Y1f + Y2Y2f)", "mime": "application/pdf"}, {"id": "ejde-338", "words": "10033", "extension": ".pdf", "flesch": "81", "author": "Lv, Huilin; Zheng, Shenzhou; Feng, Zhaosheng", "title": "Existence results for nonlinear Schrodinger equations involving the fractional (p,q)-Laplacian and critical nonlinearities", "date": "2021", "keywords": "lemma; proof; q\u2217s2", "summary": "Let vn = un \u2212 u and J\u03b5(vn) \u2192 d. By Brezis-Lieb Lemma in [11] and [28, Lemma 3.3] we find that |vn| q\u2217s2 q\u2217s2 = |un| q\u2217s2 q\u2217s2 \u2212 |u| q\u2217s2 q\u2217s2 + on(1). Indeed, we would like to stress that standard arguments used to investigate the linear case p = q = 2 seem to be inapplicable to the nonlinear case on account of EJDE-2021/100 EXISTENCE RESULTS FOR NONLINEAR SCHRO\u0308DINGER EQUATIONS 3 the lack of Hilbertian structure of W s,p(Rn) for p 6= 2.", "mime": "application/pdf"}, {"id": "ejde-339", "words": "10091", "extension": ".pdf", "flesch": "88", "author": "Bhimani, Divyang G.", "title": "Global well-posedness for Klein-Gordon-Hartree and fractional Hartree equations on modulation spaces", "date": "2021", "keywords": "modulation; mp,1; proposition; spaces", "summary": "= (V \u2217 |u|2), u(0) = u0, ut(0) = u1, (1.2) where u(t, x) is a complex valued function of (t, x) \u2208 R \u00d7 Rd, i = \u221a \u22121, ut = \u2202 \u2202t , utt = \u22022 \u22022t , I is the identity operator, \u2206 is the Laplace operator, u0 and u1 are complex valued functions of x \u2208 Rd, \u2217 denotes the convolution in Rd, and V is of the type V (x) = \u03bb |x|\u03b3 , \u03bb \u2208 R, x \u2208 Rd, 0 < \u03b3 < d. (1.3) The stationary equation \u2212\u2206u+(V \u2217|u|2)u = \u222b Rd f(w) e2\u03c0ix\u00b7wdw, x \u2208 Rd, and", "mime": "application/pdf"}, {"id": "ejde-34", "words": "5794", "extension": ".pdf", "flesch": "83", "author": "Tong, Zhi-Juan; Chen, Jianqing; Wang, Zhi-Qiang", "title": "Non-radial normalized solutions for a nonlinear Schrodinger equation", "date": "2023", "keywords": "lim; solutions", "summary": "Choose nm \u2192\u221e, as m\u2192\u221e such that \u2223\u2223bm \u2212 \u222b TRm |unm |2dx \u2223\u2223 \u2264 1 m , \u2223\u2223\u2223bm+1 \u2212 \u222b TRm+1 |unm |2dx \u2223\u2223\u2223 \u2264 1 m . \u2212 C0 rn = (\u2016vn\u201622 2b \u222b RN \u2223\u2223\u221ab\u2207vn \u2016 vn\u20162 \u2223\u22232 \u2212 \u2016vn\u2016p2 pbp/2 \u222b RN \u2223\u2223\u221abvn \u2016vn\u2016 2 \u2223\u2223pdx) + (\u2016\u03c9n\u201622 2b \u222b RN \u2223\u2223\u221ab\u2207\u03c9n \u2016\u03c9n\u20162 \u2223\u22232 \u2212 \u2016\u03c9n\u2016p2 pbp/2 \u222b RN \u2223\u2223\u221ab\u03c9n \u2016\u03c9n\u2016 2 \u2223\u2223pdx)\u2212 C0 rn \u2265 \u2016vn\u2016 2 2 b S(Rn, b) + (\u2016vn\u201622 pb \u2212 \u2016vn\u2016 p 2 pbp/2 )\u222b RN \u2223\u2223\u221abvn \u2016vn\u20162 \u2223\u2223pdx+ \u2016\u03c9n\u201622 b S(Rn, b)\u2212 C0 rn .", "mime": "application/pdf"}, {"id": "ejde-340", "words": "3928", "extension": ".pdf", "flesch": "90", "author": "Xia, Pengcheng; Su, Yu", "title": "p-Laplacian equation with finitely many critical nonlinearities", "date": "2021", "keywords": "d1,p(rn", "summary": "By Lemma 3.1, there exists tv\u0304 > 0 such that tv\u0304 v\u0304 \u2208 N \u03b6 . Introduction We consider the p-Laplacian equation \u2212\u2206pu\u2212 \u03b6 |u|p\u22122u |x|p = k\u2211 i=1 ( I\u03b1i \u2217 |u| p\u2217\u03b1i ) |u|p \u2217 \u03b1i \u22122u+ |u|p \u2217\u22122u, x \u2208 RN , (1.1) where N > 3, p \u2208 (1, N), \u03b6 \u2208 (0,\u039b), \u039b = (N\u2212pp )p, \u2206p := div(|\u2207u|p\u22122\u2207u) is the p-Laplacian, p\u2217\u03b1i = p 2 (N+\u03b1i N\u2212p ) are the Hardy-Littlewood-Sobolev critical upper exponents, and the parameters \u03b1i satisfy the following assumption: (H1) 0", "mime": "application/pdf"}, {"id": "ejde-341", "words": "5914", "extension": ".pdf", "flesch": "88", "author": "Zhu, Min; Wang, Ying; Chen, Lei", "title": "Curvature blow-up for the periodic CH-mCH-Novikov equation", "date": "2021", "keywords": "equation; u\u03022; u\u0302x", "summary": "Preliminaries To discuss the wave breaking phenomenon of the periodic CH-mCH-Novikov equation (1.1), we rewrite it as ut = \u2212k1G \u2217 (2uxm+ umx)\u2212 k2G \u2217 ((u2 \u2212 u2x)m)x \u2212 k3G \u2217 (u2mx + 3uuxm), t > 0, x \u2208 S, u(0, x) = u0(x), x \u2208 S, (2.1) where G(x) = cosh(x\u2212[x]\u2212 1 2 ) 2 sinh(1/2) , [x] represents the largest integer part of x, and G(x) is the fundamental solution of (1 \u2212 \u22022x)\u22121 on the unit circle S = R/Z, that is for any x \u2208 S. Let G(x) = \u039b1(x)+\u039b2(x), where \u039b1(x) = ex\u2212[x]\u2212 1 2 4 sinh( 1 2 ) and \u039b2(x) [\u039b1 \u2217 (u\u2212 ux)3 \u2212 \u039b2 \u2217 (u+ ux)3] \u2212 k1[\u039b2 \u2217 (u2 + 1 2 u2x)\u2212 \u039b1 \u2217 (u2 + 1 2 u2x)], u\u0302x \u2032 (t) = k1(u\u03022 \u2212 1 2 u\u0302x 2 ) + k2( 1 3 u\u03023 \u2212 u\u0302u\u0302x2) + k3u\u0302 2 (u\u03022 \u2212 u\u0302x2) \u2212 ( k2 3 + k3 2 )", "mime": "application/pdf"}, {"id": "ejde-342", "words": "8812", "extension": ".pdf", "flesch": "77", "author": "Zhao, Qingjian; Shi, Shaoyun; Li, Wenlei", "title": "Dynamics of flocking models with two species", "date": "2021", "keywords": "agents; flocking; groups; interaction; j=1; model; system", "summary": "\u2208M. With the assumptions (A1) and (A3), by differentiat- ing H(x, u, y, v) along the solution with the respect of time, we have H\u0307 = 1 2 \u2211 k 6=l \u03c6(\u2016xk \u2212 xl\u2016 \u2212 d1)\u3008~e(xk, xl), \u03c6ij = \uf8f1\uf8f4\uf8f2\uf8f4\uf8f3 \u03c61(\u2016qj \u2212 qi\u2016) = \u03c11(\u2016qj \u2212 qi\u2016)\u03c6\u0302(\u2016qj \u2212 qi\u2016 \u2212 d1), i, j = 1, . .", "mime": "application/pdf"}, {"id": "ejde-345", "words": "6507", "extension": ".pdf", "flesch": "80", "author": "Pinelas, Sandra; Tun\u00e7, Osman; Korkmaz, Erdal; Tun\u00e7, Cemil", "title": "Existence and stabilization for impulsive differential equations of second order with multiple delays", "date": "2024", "keywords": "differential; equations; i=1; n\u2211 i=1; t t0; tunc\u0327", "summary": "= { \u03c8(t), t0 \u2264 t \u2264 t0 \u2212 \u03c4N y1(t), t0 \u2264 t \u2264 T is a solution of (1.8), for all t \u2208 I. Let I1 = [t1 \u2212 \u03c4N , T ]. It follows that N\u2211 i=1 (\u03c4i) \u2264 t1 \u2212 t0 \u2264 \u00af\u0300, d\u03041 = p\u03041 \u2212 N\u2211 i=1 \u03c4i(gi + a0\u03c3i).", "mime": "application/pdf"}, {"id": "ejde-349", "words": "6457", "extension": ".pdf", "flesch": "83", "author": "Mustafa, Muhammad I.", "title": "Optimal energy decay rates for viscoelastic wave equations with nonlinearity of variable exponent", "date": "2023", "keywords": "2m1\u22122; e(t; \u222b t; \u222b \u03c9", "summary": "\u2264 \u2212 (\u222b t 0 g(s)ds\u2212 \u03b4 )\u222b \u2126 u2 t dx+ \u03b4 \u222b \u2126 |\u2207u|2 dx+ c[C\u03b1 + 1] \u03b4 (h \u25e6 \u2207u)(t) + c\u03b4(g \u25e6 \u2207u)(t) + a2 4 \u222b \u2126\u2217 |ut|2m(x)\u22122 dx+ a \u222b \u2126 C\u03b4(x)|ut|m(x) dx. (3.7) Proof. [see (2.4)], then the use of hypothesis (2.2), (3.1), and Jensen\u2019s inequality leads to\u222b t 0 g(s) \u222b \u2126 |\u2207u(t)\u2212\u2207u(t\u2212 s)|2 dx ds \u2264 I(t) I(t) \u222b t 0 H \u22121 (\u2212g\u2032(s) \u03be(s) )\u222b \u2126 |\u2207u(t)\u2212\u2207u(t\u2212 s)|2 dx ds \u2264 I(t)H \u22121 ( 1 I(t) \u222b t 0 (\u2212g\u2032(s) \u03be(s) )\u222b \u2126 |\u2207u(t)\u2212\u2207u(t\u2212 s)|2 dx ds ) \u2264 I(t)H \u22121 ( 1 I(t)\u03be(t) \u222b t 0 ( \u2212 g\u2032(s) )\u222b \u2126 |\u2207u(t)\u2212\u2207u(t\u2212 s)|2 dx ds ) \u2264 I(t)H \u22121 (\u22122E\u2032(t) I(t)\u03be(t) ) .", "mime": "application/pdf"}, {"id": "ejde-350", "words": "6949", "extension": ".pdf", "flesch": "82", "author": "Su, Yu; Chen, Haibo; Liu, Senli; Fang, Xianwen", "title": "Fractional Schrodinger-Poisson systems with weighted Hardy potential and critical exponent", "date": "2020", "keywords": "ds,2; lim; rad(r3; schro\u0308dinger; system", "summary": "= \u03bb 3\u22122s 2 n un(\u03bbnx+ xn) where \u03bbn > 0, xn \u2208 R3 and xn \u03bbn \u2192\u221e as n\u2192 +\u221e, they derived that vn \u21c0 v in Ds,2(R3) and\u222b R3 vk\u03c6 |x+ xk \u03bbk |2s \u2192 0 as k \u2192 +\u221e (1.10) for any \u03c6 \u2208 Ds,2(R3). In particular the Schro\u0308dinger equa- tion for the wave function of an electron interacting with a polar molecule (supposed to be point-like) can be written as H = \u2212 ~ 2m \u2206 + e x \u00b7D |x|3 \u2212 E, where D is the dipole moment of the molecule, e and m denote the charge and the mass of the electron (see [26]).", "mime": "application/pdf"}, {"id": "ejde-352", "words": "6722", "extension": ".pdf", "flesch": "82", "author": "Wu, Hong-Jie; Han, Bang-Sheng; Mi, Shao-Yue; Shen, Liang-Bin", "title": "Traveling wave solutions for three-species nonlocal competitive-cooperative systems", "date": "2023", "keywords": "lim; species; u(x; v(x; w(x; wave", "summary": "+ [e\u2212\u03bbcx \u2212Ae\u2212(\u03bbc+\u03b5)x](Zc1e \u2212\u03bbcx + b1e \u2212\u03b6cx + c1e \u2212\u03b7cx) < \u2212A\u03bace\u2212(\u03bbc+\u03b5)x + e\u2212\u03bbcx(Zc1e \u2212\u03bbcx + b1e \u2212\u03b6cx + c1e \u2212\u03b7cx) = e\u2212(\u03bbc+\u03b5)x[\u2212A\u03bac + Zc1e \u2212(\u03bbc\u2212\u03b5)x + b1e \u2212(\u03b6c\u2212\u03b5)x + c1e \u2212(\u03b7c\u2212\u03b5)x] < 0, \u2212 d2q\u2032\u2032c \u2212 cq \u2032 c \u2212 r2qc + r2qc(\u03c62 \u2217 qc)\u2212 b2r2qclc + c2r2qcpc = (\u2212d2\u03b62c + c\u03b6c \u2212 r2)e\u2212\u03b6cx +Be\u2212(\u03b6c+\u03b5)x[d2(\u03b6c + \u03b5)2 \u2212 c(\u03b6c + \u03b5) + r2] + r2[e\u2212\u03b6cx \u2212Be\u2212(\u03b6c+\u03b5)x] ( Zc2e \u2212\u03b6cx \u2212 b2e\u2212\u03b7cx + b2De \u2212(\u03b7c+\u03b5)x + c2e \u2212\u03bbcx ) < e\u2212(\u03b6c+\u03b5)x[\u2212B\u03b9c + r2Z c 2e \u2212(\u03b6c\u2212\u03b5)x + r2b2De \u2212\u03b7cx + r2c2e \u2212(\u03bbc\u2212\u03b5)x] < 0, and \u2212 d3l\u2032\u2032c \u2212 cl \u2032 c \u2212 r3lc + r3lc(\u03c63 \u2217 lc)\u2212 b3r3lcqc + c3r3lcpc = (\u2212d3\u03b72c + c\u03b7c \u2212 r3)e\u2212\u03b7cx +De\u2212(\u03b7c+\u03b5)x[d3(\u03b7c + \u03b5)2 \u2212 c(\u03b7c + \u03b5) + r3] + r3[e\u2212\u03b7cx On the other hand, combining with (2.3)-(2.5), it is easy to calculate \u2212 p\u0303\u2032\u2032c \u2212 cp\u0303\u2032c + (\u03c61 \u2217 u0 + b1v0 + c1w0)p\u0303c \u2264 \u2212p\u0303\u2032\u2032c", "mime": "application/pdf"}, {"id": "ejde-353", "words": "7999", "extension": ".pdf", "flesch": "82", "author": "Li, Yuxin; Chang, Xiaojun; Feng, Zhaosheng", "title": "Normalized solutions for Sobolev critical Schrodinger-Bopp-Podolsky systems", "date": "2023", "keywords": "m(c; podolsky; schro\u0308dinger; solutions; system", "summary": "For c \u2208 (0, c0), I(u) restricted to \u039b(c) is coercive on H1(R3). They showed that system (1.3) admits ground state solutions under certain conditions of V and f .", "mime": "application/pdf"}, {"id": "ejde-354", "words": "4489", "extension": ".pdf", "flesch": "78", "author": "Purushothaman, Ganesh; Suresh, Kannan; Tunc, Ercan; Thandapani, Ethiraju", "title": "Oscillation criteria of fourth-order nonlinear semi-noncanonical neutral differential equations via a canonical transform", "date": "2023", "keywords": "differential; equations; order; y(t", "summary": "[14] N. Kilinc Gecer, P. Temtek; Oscillation criteria for fourth order differential equations, J. Inst. Then (i) if y(t) \u2208 S1, then y(t) A1(t) is decreasing for t \u2265 t1 for some t1 \u2265 t0; (ii) if y(t) \u2208 S3, then y(t) Q3(t) is decreasing and L1y(t) \u2265 Q2(t)L3y(t) for t \u2265 t1 for some t1 \u2265 t0.", "mime": "application/pdf"}, {"id": "ejde-355", "words": "8442", "extension": ".pdf", "flesch": "75", "author": "Musolino, Paolo; Dutko, Martin; Mishuris, Gennady", "title": "Asymptotic analysis of perturbed Robin problems in a planar domain", "date": "2023", "keywords": "log; log \u03b5; problem; \u03b5\u03b4(\u03b5; \u03c1(\u03b5; \u2202\u03c9i; \u2202\u03c9o", "summary": "Boundary value problems with degenerating or perturbed boundary conditions have been analyzed by many authors. Singularly perturbed boundary value problem; Laplace equation; nonlinear Robin condition; perforated planar domain; integral equation.", "mime": "application/pdf"}, {"id": "ejde-356", "words": "5830", "extension": ".pdf", "flesch": "69", "author": "Feckan, Michal; Marynets, Kateryna", "title": "Non-local fractional boundary value problems with applications to predator-prey models", "date": "2023", "keywords": "t t", "summary": "Let us fix values of parameters \u03be \u2208 D\u03be and \u03b7 \u2208 D\u03b7 and show that {uqm(t, \u03be, \u03b7) : t \u2208 = \u222a\u03be\u2208D\u039e\u03c1(\u03be), \u039e\u03c1(\u03be) := {\u03be \u2208 Rn : |\u03be \u2212 z| \u2264 \u03c1}for all \u03be. (A3)", "mime": "application/pdf"}, {"id": "ejde-36", "words": "9360", "extension": ".pdf", "flesch": "75", "author": "Xiao, Qingkun; Gao, Hongjun", "title": "Stochastic attractor bifurcation for the two-dimensional Swift-Hohenberg equation with multiplicative noise", "date": "2023", "keywords": "al(\u03b8t\u03c9; bifurcation; equation; stochastic", "summary": "\u03be3 \u2212 3 2 \u03be33 \u2212 3\u03be21\u03be3 \u2212 3\u03be22\u03be3 \u2212 3\u03be3\u03be 2 4 \u2212 3 2 \u03be21\u03be4 + 3 2 \u03be22\u03be4)dt+ \u03c3\u03be3 \u25e6 dWt, d\u03be4 = (P ( \u221a 2\u03c0 L )\u03be4 \u2212 3 2 \u03be34 \u2212 3\u03be21\u03be4 \u2212 3\u03be22\u03be4 \u2212 3\u03be23\u03be4 \u2212 3 2 \u03be21\u03be3 + 3 2 \u03be22\u03be3)dt+ \u03c3\u03be4 \u25e6 dWt. \u03be1 \u2212 3 2 \u03be31 \u2212 3\u03be1\u03be 2 2 \u2212 3\u03be1\u03be 2 3 \u2212 3\u03be1\u03be 2 4)dt+ \u03c3\u03be1 \u25e6 dWt, (5.8) d\u03be2 = (P ( \u221a m2 + n2\u03c0 L )\u03be2 \u2212 3 2 \u03be32 \u2212 3\u03be21\u03be2 \u2212 3\u03be2\u03be 2 3 \u2212 3\u03be2\u03be 2 4)dt+ \u03c3\u03be2 \u25e6 dWt, (5.9) d\u03be3 = (P ( \u221a m2 + n2\u03c0 L )\u03be3 \u2212 3 2 \u03be33 \u2212 3\u03be21\u03be3 \u2212 3\u03be22\u03be3 \u2212 3\u03be3\u03be 2 4)dt+ \u03c3\u03be3 \u25e6 dWt, (5.10) d\u03be4 = (P ( \u221a m2 + n2\u03c0 L )\u03be4 \u2212 3 2 \u03be34 \u2212 3\u03be21\u03be4 \u2212 3\u03be22\u03be4 \u2212 3\u03be23\u03be4)dt+ \u03c3\u03be4 \u25e6 dWt.", "mime": "application/pdf"}, {"id": "ejde-360", "words": "9277", "extension": ".pdf", "flesch": "75", "author": "Shillor, Meir; Kadhim, Thanaa Ali", "title": "Analysis and simulations of the HANDY model with social mobility, renewables and nonrenewables", "date": "2023", "keywords": "case; model; states; system; wealth", "summary": "\u2212 \u03b3c, J12 = \u03b3e, J13 = 0, J14 = 0, J15 = 0. J21 = \u03b3c, J22 = \u03b2e \u2212 \u03b1m \u2212 \u03b3e, J23 = 0, J24 = 0, J25 = 0. Then, Cc = \u03b7sxc, Ce = \u03b7\u03ba1sxe, and \u03b1c = \u03b1M \u2212 \u03b7(\u03b1M \u2212 \u03b1m), \u03b1e = \u03b1M \u2212 \u03ba1\u03b7(\u03b1M", "mime": "application/pdf"}, {"id": "ejde-361", "words": "9338", "extension": ".pdf", "flesch": "78", "author": "Liu, Mengqian; Wu, Zhigang", "title": "Space-time behavior for radiative hydrodynamics model with or without heat conduction", "date": "2023", "keywords": "4w\u03043; cv(2\u00b5+; function; green; pointwise; |\u03be|2", "summary": "\u2212 \u03bd2g1 \u2212 \u03bd1g3. + \u00b7 \u00b7 \u00b7 , G\u030212 = \u2212i R(\u03ba\u03c1\u0304 + 4w\u03043 C3 v \u03c1\u0304 4 ) c2Cv(Cv +R) \u03beT e\u03bb1t \u2212 1 2c \u03beT |\u03be| (e\u03bb2t \u2212 e\u03bb3t) + \u00b7 \u00b7 \u00b7 , G\u030213 = \u2212 R c2Cv e\u03bb1t + R 2c2Cv (e\u03bb2t + e\u03bb3t) + \u00b7 \u00b7 \u00b7 , G\u030221 = \u2212i (\u03ba\u03c1\u0304 + 4w\u03043 C3 v \u03c1\u0304 4 ) Cv +R \u03bee\u03bb1t", "mime": "application/pdf"}, {"id": "ejde-362", "words": "4748", "extension": ".pdf", "flesch": "81", "author": "Drissi, Amor; Ghanmi, Abdeljabbar; Repovs, Dusan D.", "title": "Singular p-biharmonic problems involving the Hardy-Sobolev exponent", "date": "2023", "keywords": "p\u2217(\u03b1", "summary": "dx\u2212 1 p\u2217(\u03b1) S \u2212 p \u2217(\u03b1) p p\u2217 \u2016\u03d5\u2016p \u2217(\u03b1) \u2265 1 p \u2016\u03d5\u2016p \u2212 \u00b5 r c1\u2016\u03d5\u2016rr,f \u2212 1 p\u2217(\u03b1) S \u2212 p \u2217(\u03b1) p p\u2217 \u2016\u03d5\u2016p \u2217(\u03b1) \u2265 1 p \u2016\u03d5\u2016p \u2212 \u00b5 r c1\u2016f\u2016 p\u2217 p\u2217\u2212r S \u2212r/p p\u2217 \u2016\u03d5\u2016r \u2212 1 p\u2217(\u03b1) dx \u2212 p\u2217(\u03b1) p\u2217(\u03b1) \u222b RN |x|\u2212\u03b1\u03d5p \u2217(\u03b1)", "mime": "application/pdf"}, {"id": "ejde-363", "words": "3847", "extension": ".pdf", "flesch": "81", "author": "Alsaedi, Ahmed; Ahmad, Bashir; Kirane, Mokhtar; Nabti, Aberrazak", "title": "Lifespan of solutions of a fractional evolution equation with higher order diffusion on the Heisenberg group", "date": "2020", "keywords": "r2n+1", "summary": "A function u is called a local weak solution of (1.1)\u2013 (1.2), if u \u2208 C([0, T );Lploc(R2N+1)) and satisfies \u03bb \u222b T 0 \u222b R2N+1 I\u03b10|t|u| p\u03c6(\u03b7, t) d\u03b7 [13] considered the equation i\u2202tu+ \u2206u = \u03bb \u0393(\u03b1) \u222b t 0 (t\u2212 s)\u03b1\u22121|u(s)|p ds, x \u2208 RN , t > 0, (1.4) with u(x, 0) = f(x), f \u2208 L1(RN ) and proved that if 1 < p \u2264 1+2(\u03b1+1)/(N\u22122\u03b1)+, \u03bb \u2208 C\\{0}, \u03bb1 > 0 and \u222b RN f2(x) dx < 0, then equation (1.4) has no global weak solutions.", "mime": "application/pdf"}, {"id": "ejde-364", "words": "4318", "extension": ".pdf", "flesch": "83", "author": "\u00a0Allahverdiev, Bilender P.; Tuna, Huseyin", "title": "Properties of the resolvent of singular q-Dirac operators", "date": "2020", "keywords": "function; q\u2212n; resolvent", "summary": "For each non-real number \u03bb, we have \u03c7q\u2212n(x, \u03bb)\u2192 \u03c7(x, \u03bb) and\u222b q\u2212n 0 \u2016\u03c7q\u2212n(x, \u03bb)\u20162Edqx\u2192 \u222b \u221e 0 \u2016\u03c7(x, \u03bb)\u20162Edqx, n\u2192\u221e. 4 B. P. ALLAHVERDIEV, H. TUNA EJDE-2020/03 Putting Gq\u2212n(x, t, \u03bb) = { \u03c7q\u2212n(x, \u03bb)\u03d5T (t, \u03bb), t \u2264 x \u03d5(x, \u03bb)\u03c7Tq\u2212n(t, \u03bb), t > x\uf8f1\uf8f4\uf8f4\uf8f4\uf8f4\uf8f2\uf8f4\uf8f4\uf8f4\uf8f4\uf8f3 ( [\u03c7q\u2212n1(x, \u03bb)\u03d51(t, \u03bb) \u03c7q\u2212n1(x, \u03bb)\u03d52(t, \u03bb) \u03c7q\u2212n2(x, \u03bb)\u03d51(t, \u03bb) \u03c7q\u2212n2(x, \u03bb)\u03d52(t, \u03bb) ) , t \u2264 x( \u03d51(x, \u03bb)\u03c7q\u2212n1(t, \u03bb) \u03d51(x, \u03bb)\u03c7q\u2212n2(t, \u03bb) \u03d52(x, \u03bb)\u03c7q\u2212n1(t, \u03bb) \u03d52(x, \u03bb)\u03c7q\u2212n2(t, \u03bb) ) , x < t, (3.6) we have (Rq\u2212nf)(x, \u03bb) = y(x, \u03bb) = \u222b q\u2212n 0 Gq\u2212n(x, t, \u03bb)f(t)dqt, \u03bb \u2208 C, (3.7) where y(x, \u03bb) = ( y1(x, \u03bb) y2(x, \u03bb) ) and f(\u00b7) = ( f1(\u00b7) f2(\u00b7) ) \u2208 H. \u03bb \u00b5 Im{m(\u03c3 + i\u03c4)}d\u03c3, z = \u03c3 + i\u03c4, \u03c4 > 0. (5.2) Proof.", "mime": "application/pdf"}, {"id": "ejde-365", "words": "7482", "extension": ".pdf", "flesch": "86", "author": "Liu, Xiang; Jia, Baoguo; Gensler, \u00a0Scott; Erbe, Lynn; Peterson, Allan", "title": "Convergence of approximate solutions to nonlinear Caputo nabla fractional difference equations with boundary conditions", "date": "2020", "keywords": "a+1; nb\u22121", "summary": "= 0 for t \u2208 Na+1, where \u03c7[a,\u221e)(t) = { 1, t \u2208 Na, 0, t /\u2208 Then the Green function for the BVP (Lax)(t) = 0, t \u2208 Nb\u22121 a+1, x(a) = 0, x(b)", "mime": "application/pdf"}, {"id": "ejde-368", "words": "6442", "extension": ".pdf", "flesch": "85", "author": "Yao, Shuai; Sun, \u00a0Juntao; Wu, Tsung-Fang", "title": "Stationary quantum Zakharov systems involving a higher competing perturbation", "date": "2020", "keywords": "k(x)\u03c6k; \u03bb,\u00b5", "summary": "SYSTEMS 9 < p\u2212 2 4p \u2016u\u20162\u03bb for u \u2208 N (2) \u03bb,\u00b5, and so h\u2032\u2032u(1) Hence, if u \u2208 X\u03bb is a critical point of I\u03bb,\u00b5, then (u, \u03c6K,u) is a solution of system (1.4).", "mime": "application/pdf"}, {"id": "ejde-37", "words": "5794", "extension": ".pdf", "flesch": "77", "author": "Lv, Jiaojiao; Wang, Jinrong; Liu, Rui", "title": "Hyers-Ulam stability of linear quaternion-valued differential equations", "date": "2023", "keywords": "hyers; quaternion; stability; ulam", "summary": "[28] X. Zhang; Global structure of quaternion polynomial differential equations, Communications in Mathematical Physics, 303 (2011), 301\u2013316. [4, 5] studied the Hyers-Ulam stability of first-order matrix differential equations by using the norm estimation of exponential functions of quaternion matrices and derived the Hyers-Ulam stability of linear quaternion- valued differential equations by using the Laplace transform.", "mime": "application/pdf"}, {"id": "ejde-371", "words": "5768", "extension": ".pdf", "flesch": "80", "author": "Le Trong Thanh, Bui; Ngoc Quoc Thuong, Nguyen", "title": "Passing to the limit on small parameters for generalized viscous Cahn-Hilliard type equations with nonlinear source", "date": "2020", "keywords": "equation; problem", "summary": "+ \u03b5 2 |\u2207u\u03b5|2dx+ \u222b t 0 \u222b \u2126 |\u2207v\u03b5|2dx \u2264 C1 \u222b t 0 \u222b \u2126 f2(u\u03b5)dx+ C2. 12 B. L. T. THANH, N. N. Q. THUONG EJDE-2020/07 Now using assumption (H4),\u222b \u2126 \u03a6(u\u03b5) (2.24) Integrate (2.24) over (0, t) with t \u2264 T \u2217; then thanks to (2.21) we have t\u2016v\u20162\u22121 + \u03b4t\u2016v\u20162 \u2264 c \u222b t 0 (s\u2016v\u20162 + \u03b4s\u2016v\u20162)ds+ \u222b t 0 \u2016v\u20162\u22121 + \u03b4\u2016v\u20162ds (2.25) \u2264 c \u222b t 0 (s\u2016v\u20162 + \u03b4s\u2016v\u20162)ds+Q(\u2016u0\u2016H2).", "mime": "application/pdf"}, {"id": "ejde-376", "words": "12152", "extension": ".pdf", "flesch": "79", "author": "Kijowski, Antoni", "title": "Characterization of mean value harmonic functions on norm induced metric measure spaces with weighted Lebesgue measure", "date": "2020", "keywords": "functions; harmonic; mean; theorem; value", "summary": "Then for each K b \u2126\u2225\u2225\u2206hf |h| \u2225\u2225 Lp(K) \u2264 C\u2016\u2207f\u2016Lp(\u2126), for some constant C > 0 and all h \u2208 Rn, 0 < 2|h| < dist(K, \u2202\u2126). (2) Suppose that 1 < p < \u221e, K b \u2126, function f \u2208 Lp(K) and there exists constant C > 0 Harmonic function; mean value property; metric measure space; Minkowski functional; norm induced metric; Pizzetti formula; weighted Lebesgue measure.", "mime": "application/pdf"}, {"id": "ejde-379", "words": "5928", "extension": ".pdf", "flesch": "83", "author": "Zhao, Junfang; Liu, Xiangqing", "title": "Ground state solutions for quasilinear equations of Kirchhoff type", "date": "2020", "keywords": "kirchhoff; solutions; \u222b \u03c9", "summary": "Given u, \u03d5 \u2208 X with the property that \u222b \u2126 u2|\u2207\u03d5|2 dx < +\u221e and \u222b \u2126 |\u2207u|2\u03d52 dx < +\u221e, for example \u03d5 \u2208 C\u221e0 (\u2126), \u03d5 = u, u+ or u\u2212, where u+ = max{u, 0}, u\u2212 = min{u, 0}, we can define the derivative of I in the direction \u03d5 at u, denoted by \u3008DI(u), \u03d5\u3009 as \u3008DI(u), \u03d5\u3009 = lim t\u21920+ 1 t (I(u+ t\u03d5)\u2212 I(u)) For u \u2208 X, define \u03b3+(u) = \u3008DI(u), u+\u3009 = \u222b \u2126 (a|\u2207u+|2 + 2bu2 +|\u2207u+|2) dx + \u222b \u2126 (c|\u2207u|2 + du2|\u2207u|2) dx \u222b \u2126 (c|\u2207u+|2 + 2du2 +|\u2207u+|2) dx \u2212 \u222b \u2126 f(u+)u+ dx , \u03b3\u2212(u) = \u3008DI(u), u\u2212\u3009 = \u222b \u2126 (a|\u2207u\u2212|2 + 2bu2 \u2212|\u2207u\u2212|2) dx + \u222b \u2126 (c|\u2207u|2 + du2|\u2207u|2) dx \u222b \u2126 (c|\u2207u\u2212|2 + 2du2 \u2212|\u2207u\u2212|2) dx \u2212 \u222b \u2126 f(u\u2212)u\u2212 dx (1.9) and S\u2217 = {u : u \u2208 X, \u03b3+(u) = 0, u+ 6= 0; \u03b3\u2212(u) = 0, u\u2212 6= 0}, c\u2217 = inf u\u2208S\u2217 I(u) .", "mime": "application/pdf"}, {"id": "ejde-38", "words": "11780", "extension": ".pdf", "flesch": "76", "author": "Bansil, Mohit; Kitagawa, Jun", "title": "An optimal transport problem with storage fees", "date": "2023", "keywords": "function; problem; theorem; x\u00d7y; \u2212 \u222b", "summary": "Since F \u2217\u2217 \u2264 F , we also have mF\u2217\u2217 < \u221e. Then by strong duality combined with Proposition 5.1 below, we see (since F \u2217 = F \u2217\u2217\u2217) 0 By [9, Corollary 13.3.3] and since F \u2217\u2217\u2217 = F \u2217, we see that F \u2217\u2217 also has Lipschitz constant L, then a calculation similar to (6.2) with F \u2217\u2217 replacing F shows that the EJDE-2023/22 AN OPTIMAL TRANSPORT PROBLEM 23 pair (T, \u03bb\u221e) minimizes (1.2) with storage fee function F \u2217\u2217. Thus, by the strong duality Theorem 3.3 we have mF \u2212MF = mF \u2212mF\u2217\u2217 = F (\u03bb\u221e)\u2212 F \u2217\u2217(\u03bb\u221e)", "mime": "application/pdf"}, {"id": "ejde-380", "words": "6255", "extension": ".pdf", "flesch": "86", "author": "Silva, Kaye; Moreno Sousa, Steffanio", "title": "Multiplicity of positive solutions for a gradient type cooperative/competitive elliptic system", "date": "2020", "keywords": "\u03bb,\u00b5", "summary": "For \u03bb, \u00b5 \u2208 R and w \u2208 X we introduce H\u03bb,\u00b5(w) Moreover, \u03c8\u03bb,\u00b5,w is decreasing; We start with the study of N+ \u03bb,\u00b5. Observe from Proposition 2.2 that if N+ \u03bb,\u00b5 6= \u2205 then there exist (\u03bb, \u00b5) \u2208 R2 and w \u2208 X such that H\u03bb(w) < 0 or equivalently\u222b |\u2207u|2 + \u222b |\u2207v|2 \u2212 \u00b5 ( \u222b |u|2 + \u222b |v|2 ) 2 \u222b uv < \u03bb, therefore we are led to the study of the function \u03bbmin(\u00b5;w) := \u2016w\u20162 \u2212 \u00b5\u2016w\u201622 2 \u222b uv , w \u2208 X , \u222b uv > 0. (2.1)", "mime": "application/pdf"}, {"id": "ejde-381", "words": "4924", "extension": ".pdf", "flesch": "87", "author": "Milla Miranda, Manuel; Medeiros, Luiz A.; Louredo, Aldo T.", "title": "Global solutions to a quasilinear hyperbolic equation", "date": "2020", "keywords": "i=1; \u2202xi", "summary": "= \u222b t 0 u\u2032m(\u03c4)d\u03c4 + u0, we obtain that (um) is bounded in L\u221eloc(0,\u221e;H1 \u03930 (\u2126)). We obtain 1 2 d dt |u\u2032m|2 + n\u2211 i=1 ( \u03c3\u2032i (\u2202um \u2202xi )\u2202u\u2032m \u2202xi , \u2202u\u2032\u2032m \u2202xi ) + \u2016u\u2032\u2032m\u20162 + 1 2 d dt |u\u2032\u2032m|2L2(\u03931) = 0. (4.4)", "mime": "application/pdf"}, {"id": "ejde-382", "words": "8961", "extension": ".pdf", "flesch": "88", "author": "Yang, Jie; Chen, Haibo; Feng, Zhaosheng", "title": "Multiple positive solutions to the fractional Kirchhoff problem with critical indefinite nonlinearities", "date": "2020", "keywords": "lemma; problem", "summary": "= t2m \u2212 A\u0304tq \u2212 B\u0304t2 \u2217 s . I\u03bb(t+(u1 \u2212 u)(u1 \u2212 u)) \u2264 I\u03bb(u1 \u2212 u), which implies that u1 is a local minimizer of I\u03bb in E0.", "mime": "application/pdf"}, {"id": "ejde-383", "words": "8512", "extension": ".pdf", "flesch": "83", "author": "Chen, Qing; Wu, Guochun; Zhang, Yinghui; Zou, \u00a0Lan", "title": "Optimal time decay rates for the compressible Navier-Stokes system with and without Yukawa-type potential", "date": "2020", "keywords": "decay; proposition; solution; system; |\u03be|; \u2032(1", "summary": "Furthermore, we have from (2.3) that for k = l \u2212 1, \u3008\u2207l\u22121N2,\u2207l\u22121u\u3009 = \u3008\u2207l\u22121 ( \u2212 u \u00b7 \u2207u ) ,\u2207l\u22121u\u3009+ \u2329 \u2207l\u22121 ( \u2212 (P \u2032(\u03c1) \u03c1 \u2212 P \u2032(1) ) \u2207% ) ,\u2207l\u22121u \u232a + \u2329 \u2207l\u22121 (\u00b5 \u03c1 %\u2207u ) ,\u2207lu \u232a + \u2329 \u2207l\u22121 ( \u2207 (\u00b5 \u03c1 % ) \u00b7 \u2207u ) ,\u2207l\u22121u \u232a + \u2329 \u2207l\u22121 (\u00b5+ \u03bd \u03c1 %div u ) ,\u2207l\u22121 div u \u232a + \u2329 \u2207l\u22121 ( \u2207 (\u00b5+ \u03bd \u03c1 % ) div u ) ,\u2207l\u22121u \u232a . \u03b4 ( \u2016\u2207l%\u20162L2 + \u2016\u2207lu\u20162L2 ) , (4.26) EJDE-2020/102 TRAVELING WAVES FOR A CHEMOTAXIS MODEL 15 where (6.9) is used, and for k = l, \u3008\u2207lN2,\u2207lu\u3009 = \u3008\u2207l(\u2212u \u00b7 \u2207u),\u2207lu\u3009+ \u2329 \u2207l\u22121 ((P \u2032(\u03c1) \u03c1 \u2212 P \u2032(1) ) \u2207% ) ,\u2207l div u \u232a + \u2329 \u2207l\u22121 (\u00b5 \u03c1 %\u2206u ) ,\u2207l div u \u232a + \u2329 \u2207l\u22121 (\u00b5+ \u03bd \u03c1 %\u2207div u ) ,\u2207l div u \u232a .", "mime": "application/pdf"}, {"id": "ejde-385", "words": "12759", "extension": ".pdf", "flesch": "78", "author": "Li, Min", "title": "Time periodic solutions for the non-isentropic compressible quantum hydrodynamic equations with viscosity in R^3", "date": "2020", "keywords": "= \u2212; div; estimates; proof; quantum; solutions; system; time; ~2\u03c4; \u03c4\u03c1)2; \u2212 \u222b; \u222b \u03c9r", "summary": "\u2212 \u2016u\u20162L2 \u2212 2 3 \u2016\u03c1\u20162L2 \u2212 3 2 \u2016s\u20162L2 \u2212 5\u03b5 3 \u2016\u2207\u03c1\u20162L2 \u2212 \u00b5\u2016\u2207u\u20162L2 \u2212 \u03ba\u2016\u2207s\u20162L2 \u2212 \u00b5 3 \u2016div u\u20162L2 + \u03b4\u2016u\u20162L2 + C\u03c4 ( \u2016(u, \u03c1, s)\u2016L\u221e + \u2016(\u03c1, s,\u2207\u03c1)\u20162L\u221e ) \u2016(u,\u2207u,\u2207s,\u2207\u03c1)\u20162L2 + C\u03c4\u2016fR\u20162L2 + C\u03b5\u2016\u2207s\u20162L2 + C~4\u2016\u2207 div u\u20162L2 \u2264 6\u2211 i=1 R2,i \u2212 4\u03ba 3 \u222b \u2126R \u2207s \u00b7 \u2207\u03c1\u2212 2 \u222b \u2126R \u03c1s\u2212 4\u03ba 9 \u2016\u2207\u03c1\u20162L2 \u2212 \u2016u\u20162L2 \u2212 2 3 \u2016\u03c1\u20162L2 \u2212 3 2 \u2016s\u20162L2 \u2212 5\u03b5 3 \u2016\u2207\u03c1\u20162L2", "mime": "application/pdf"}, {"id": "ejde-388", "words": "7988", "extension": ".pdf", "flesch": "62", "author": "Feng, Zaichun; Li, Y. Charles", "title": "Short term unpredictability of high Reynolds number turbulence - rough dependence on initial data", "date": "2020", "keywords": "base; equations; perturbations; solutions; turbulence", "summary": "Since the perturbation equations are linear, such perturbation solutions generated from single Fourier modes form a base of superposition. Now we choose more general initial perturbations to the base solution initial condition (5.12)-(5.13) as follows du1(0)", "mime": "application/pdf"}, {"id": "ejde-389", "words": "5310", "extension": ".pdf", "flesch": "84", "author": "Kong, Huihui; Lian, Ruxu", "title": "Free boundary value problem for compressible magnetohydrodynamic equations", "date": "2020", "keywords": "a(t; \u222b b(t; \u222b t", "summary": "From (4.15)2 we find that d d\u03c4 \u222b 1 0 u(\u03be, \u03c4)d\u03be = 0, (4.17) and without loss of generality, we can renormalize \u222b 1 0 u0(\u03be)d\u03be to be zero, then we denote w = u\u2212 1 1 + \u03c4 \u222b \u03be 0 1 \u03c1 d\u03b6 + 1 1 + \u03c4 \u222b 1 0 \u222b \u03be 0 1 \u03c1 d\u03b6d\u03be. dx+ \u222b b(t) a(t) (2\u00b5+ \u03c1\u03b2)u2xdx + \u03bd \u222b b(t) a(t) H2 xdx = 0, (3.2) which leads to (3.1) after the integrating with respect to t \u2208", "mime": "application/pdf"}, {"id": "ejde-39", "words": "5440", "extension": ".pdf", "flesch": "78", "author": "Il'yasov, Yavdat; da Silva, Edcarlos Domingos; da Silva, Maxwell Lizete", "title": "Prescribed energy saddle-point solutions of nonlinear indefinite problems", "date": "2023", "keywords": "energy; g(x; nonlinear; solutions", "summary": "Then u = (u+ + u\u2212) \u2208 W, u\u00b1 \u2208 W\u00b1, and c0\u2016u\u201621 \u2264 \u2016u\u20162W \u2264 c1\u2016u\u201621, \u2200u \u2208 W , where 0 < c0, c1 < +\u221e do not depend on u \u2208 W . This by the Sobolev inequalities implies\u222b G(x, u)dx \u2264 \u03b5 2 C1\u2016u\u201621 + C2(\u03b5)\u2016u\u2016\u03b31 , u \u2208W, (3.1) 6 Y. IL\u2019YASOV, E. D. SILVA, M. L. SILVA EJDE-2023/23 where C1, C2(\u03b5) \u2208 (0,+\u221e) do not depend on u \u2208 W and C1 does not depend on \u03b5 > 0.", "mime": "application/pdf"}, {"id": "ejde-390", "words": "8954", "extension": ".pdf", "flesch": "82", "author": "Papageorgiou, Nikolaos S.; Vetro, Calogero; Vetro, Francesca", "title": "Positive and nodal solutions for nonlinear nonhomogeneous parametric Neumann problems", "date": "2020", "keywords": "1,p(\u03c9; a.a; f(z", "summary": "If u\u0303\u03bb 6= u\u0302\u03bb, then we can find z0 \u2208 \u2126 such that u\u0302\u03bb(z0) < u\u0303\u03bb(z0) implies u\u0302\u03bb(z0) < u\u0302\u03bbn(z0) for all n \u2265 n0 (see (3.52)). By Proposition 3.2, we can find u\u03b8 \u2208 S\u03b8 \u2286 D+, u0 \u2208 S\u03bb \u2286 D+ and u\u03b7 \u2208 S\u03b7 \u2286 D+ such that u\u03b8 \u2212 u0 \u2208 int C\u0302+ and u0 \u2212 u\u03b7 \u2208 int C\u0302+, \u21d2 u0 \u2208 intC1(\u2126)[u\u03b7, u\u03b8].", "mime": "application/pdf"}, {"id": "ejde-392", "words": "10906", "extension": ".pdf", "flesch": "79", "author": "Tian, Hong; Zheng, \u00a0Shenzhou", "title": "Orlicz estimates for general parabolic obstacle problems with p(t,x)-growth in Reifenberg domains", "date": "2020", "keywords": "p(t; parabolic", "summary": "Therefore, from (3.20) it follows that \u2212 \u222b K5 zi |Dw|2p(t,x)\u2212pi dx dt \u2264 \u2212 \u222b K5 zi |Dw|p(t,x)(1+\u03c9(\u0393(48\u03c7\u03c1i) \u03b1)) By Lemma 3.5 it holds \u2212 \u222b K\u03ba 4r(z) |Dw|p(t,x) dx dt \u2264 c2\u03ba with c2 > 1.", "mime": "application/pdf"}, {"id": "ejde-394", "words": "5895", "extension": ".pdf", "flesch": "77", "author": "Fang, Yue; Li, Kaiqiang; Xu, Xin", "title": "Global classical solutions to equatorial shallow-water equations", "date": "2023", "keywords": "t)3/2", "summary": "+ 1 8 \u2016\u03c9y\u20162. (3.47) Similar derivations show that\u222b \u2126 \u03c9y\u2207 \u00b7 U dx \u2264 \u2016\u03c9y\u2016\u2016\u2207 \u00b7 U\u2016 \u2264 \u2016\u03c9y\u2016\u2016U\u20161 \u2264 C3 ( W (t)3/2 + E(t) + \u2016\u03c9\u20162 ) + 1 8 \u2016\u03c9y\u20162. Since \u222b \u2126 \u03c9ttU \u00b7 \u2207\u03c9tt dx = \u222b \u2126 \u2207 \u00b7 (\u03c9 2 tt 2 U)\u2212 \u03c92 tt 2 \u2207 \u00b7 U dx = \u2212 \u222b \u2126 \u03c92 tt 2 \u2207 \u00b7 U dx \u2264 C3W (t)3/2, (3.56) and\u222b \u2126 y\u03c9tt\u2207 \u00b7", "mime": "application/pdf"}, {"id": "ejde-395", "words": "6064", "extension": ".pdf", "flesch": "83", "author": "Yan Xu, Hong; Tu, Jin", "title": "Existence of rational solutions for q-difference Painleve equations", "date": "2020", "keywords": "difference; equations; f(z", "summary": "[14] R. Korhonen, Z. T. Wen; Existence of zero-order meromorphic solutions in detecting q- difference Painleve\u0301 equations, Trans. [19] Z. T. Wen; Meromorphic solutions to difference Painleve\u0301 equations I and II, Electronic J. Diff.", "mime": "application/pdf"}, {"id": "ejde-396", "words": "6197", "extension": ".pdf", "flesch": "85", "author": "Cao Labora, Daniel; Rodriguez-Lopez, Rosana; Belmekki, \u00a0Mohammed", "title": "Existence of solutions to nonlocal boundary value problems for fractional differential equations with impulses", "date": "2020", "keywords": "\u03b2(1\u2212 t1; \u2212 \u03b2(1\u2212", "summary": "= \uf8f1\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f2\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f3 B [ \u2212 \u03b10(\u03be0 \u2212 s)\u03b4\u22121(\u03b4 \u2212 \u03b2(1\u2212 t1)) \u2212\u03b11\u03b2(1\u2212 t1)1\u2212\u03b4(\u03be1 \u2212 t1)\u03b4\u22121(t1 \u2212 s)\u03b4 ] +B\u03b2(t1 \u2212 s)\u03b4, 0 \u2264 s \u2264 \u03be0, B[\u2212\u03b11\u03b2(1\u2212 t1)1\u2212\u03b4(\u03be1 \u2212 t1)\u03b4\u22121(t1 \u2212 s)\u03b4 + \u03b2(t1 \u2212 s)\u03b4], 0 \u2264 \u03be0 \u2264 s \u2264 t1, \u2212B\u03b11(\u03be1 \u2212 s)\u03b4\u22121(\u03b4 \u2212 \u03b2(1\u2212 t1)) \u2212 t1)\u03b4\u22121(t1 \u2212 s)\u03b4 + \u03b2(t1 \u2212 s)\u03b4] if 0 \u2264 \u03be0 \u2264 t < s \u2264 t1 \u2212C\u03b11(\u03be1 \u2212 s)\u03b4\u22121(\u03b4 \u2212 \u03b2(1\u2212 t1))", "mime": "application/pdf"}, {"id": "ejde-397", "words": "31503", "extension": ".pdf", "flesch": "73", "author": "Kostic, Marko", "title": "Abstract degenerate Volterra inclusions in locally convex spaces", "date": "2023", "keywords": "abstract; degenerate; equations; f \u2208; families; family; following; function; k \u2208; linear; mlo; n \u2208; operator; p \u2208; resolvent; solution; subgenerator; t \u2208; theorem; y \u2208; \u03bb \u2208; \u2208 c; \u2208 c([0,\u221e; \u2208 d(a; \u2208 l(x; \u2208 l1; \u2208 \u03c9", "summary": "Then the mapping t 7\u2192 R(t), t \u2208 (0, \u03c4) is infinitely differentiable in L(X) and, for every compact set K \u2286 (0, \u03c4), there exists hK > 0 such that the set {h n K dn dtnR(t) Mn : t \u2208 K, n \u2208 N0} is equicontinuous. \u2208 A, t \u2208", "mime": "application/pdf"}, {"id": "ejde-398", "words": "4753", "extension": ".pdf", "flesch": "84", "author": "Dou, Xuechao; Sun, Juntao", "title": "Local well-posedness and standing waves with prescribed mass for Schrodinger-Poisson systems with a logarithmic potential in R^2", "date": "2023", "keywords": "poisson; schro\u0308dinger", "summary": "Inspired by [24], Cingolani and Weth [11] developed a variational framework of ((1.3) with W (x) \u2261 0 in the smaller Hilbert space X := { u \u2208 H1(R2) : \u222b R2 ln(1 + |x|)u2dx <\u221e } , endowed with the norm \u2016u\u20162X := \u222b R2 (|\u2207u|2 + u2(1 + ln(1 + |x|2))) dx dy \u2212 \u222b R2 F (u) dx. (1.5) under the constraint S(c) := { u \u2208 H : \u222b R2 u2dx = c } , where H := { u \u2208 H1(R2) : \u222b R2 ln(1 + |x|2)u2dx <\u221e } , endowed with the norm \u2016u\u2016H := \u2016u\u2016H1 + \u2016u\u2016\u2217, here \u2016u\u20162\u2217 = \u222b R2 ln(1 + |x|2)u2dx.", "mime": "application/pdf"}, {"id": "ejde-4", "words": "6444", "extension": ".pdf", "flesch": "83", "author": "Zhang, Mengqing; Tian, Jing; Zou, Keyue", "title": "Asymptotic stability of a stochastic age-structured cooperative Lotka-Volterra system with Poisson jumps", "date": "2023", "keywords": "solution; sup; system; t tk; x(t", "summary": "t 0 E sup s\u2208[0,t] |X(r)\u2212 x(r)|2ds + ((2\u03bb1 + 1)L2 1 + 2\u03c12 1 + 1)E \u222b t 0 |\u03a8(s)\u2212 \u03c8\u0304(s)|2ds + E sup s\u2208[0,t] \u222b t 0 2(X(s)\u2212 x(s), (G1x(\u03a8(s))\u2212G1x(\u03c8\u0304(s)))dw(s)) + 2E sup s\u2208[0,t] \u222b t 0 (X(s)\u2212 x(s), (J1x(\u03a8(s))\u2212 J1x(\u03c8\u0304(s)))dN\u0303(s)). (4.1) By the BDG inequality, we have E sup s\u2208[0,t] \u222b = \u2212 \u222b t tk \u2202x(s) \u2202a ds+ \u222b t tk [H1x +H2x]ds+ \u222b t tk G1xdw(s) + \u222b t tk J1xdN(s), thus |x(t)\u2212 x\u0304(t)|2 \u2264 4| \u222b t tk \u2202x(s) \u2202a ds|2 + 4| \u222b t tk [H1x +H2x]ds|2 + 4| \u222b t tk G1xdw(s)|2 + 4| \u222b t tk J1xdN(s)|2 \u2264 4\u2206 \u222b t tk |\u2202x(s) \u2202a |2ds+ 4\u2206 \u222b t tk |H1x +H2x|2ds+ 4| \u222b t tk G1xdw(s)|2 + 8|\u03bb1 \u222b t tk J1xds|2 \u2264 4\u2206 \u222b t tk |\u2202x(s) \u2202a |2ds+ 8\u2206[ \u222b t tk (|H2 1x|+ |H2 2x|)ds] + 4| \u222b t tk G1xdw(s)|2 + 8| \u222b t tk J1xdN\u0304(s)|2 + 8|\u03bb1 \u222b t tk J1xds|2. by Lemma 3.1, E sup t\u2208[0,T ] |x(t)\u2212 x\u0304(t)|2 \u2264 5E sup t\u2208[0,T ] max k=0,1,...,N\u22121 \u2223\u2223 \u222b t tk G1x(\u03c8)dw(s) \u2223\u22232 + 8E sup t\u2208[0,T ] max k=0,1,...,N\u22121 \u2223\u2223 \u222b t tk J1x(\u03c8)dN\u0303(s) \u2223\u22232 + 5\u2206 \u222b t tk |\u2202x(s) \u2202a |2ds+ 8TC[L2 1 + 2\u03c11 + 8\u03bb2 1L 2 1]\u2206. 12 M. ZHANG, J. TIAN, K. ZOU EJDE-2023/02 According to the Doob inequality, we obtain E sup t\u2208[0,T ] |x(t)\u2212 x\u0304(t)|2 \u2264 5\u2206 \u222b t tk |\u2202x(s) \u2202a |2ds+ 8TC[L2 1 + 2\u03c11 + 8\u03bb2 1L 2 1]\u2206 + 5 max k=0,1,...,N\u22121 \u222b (k+1)\u2206 k\u2206 E|G1x(x, y)|2ds + 8\u03bb1 max k=0,1,...,N\u22121 \u222b (k+1)\u2206 k\u2206 E|J1x(x, y)|2ds \u2264 5\u2206 \u222b t tk |\u2202x(s) \u2202a |2ds+ 8TC[L2 1 + 2\u03c11 + 8\u03bb2 1L 2 1]\u2206 + 5L2 1C\u2206 + 8\u03bb1L 2 1C\u2206. (3.7)", "mime": "application/pdf"}, {"id": "ejde-40", "words": "6752", "extension": ".pdf", "flesch": "65", "author": "Chicone, Carmen; Swanson, Richard", "title": "Linearization via the Lie derivative", "date": "2000", "keywords": "linearization; origin; theorem; vector", "summary": "= 0, \u2022 the partial derivatives Fx and Fy are Lipschitz in \u2126, and \u2022 the partial derivative Fz is Lipschitz in \u2126xy uniformly with respect to z \u2208 \u2126z and Ho\u0308lder in \u2126z uniformly with respect to (x, y) \u2208 \u2126xy with Ho\u0308lder exponent \u00b5. System (3.6) satisfies the (1, \u00b5) spectral gap condition if (1 + \u00b5)c < b. We will show that system (3.6) can be linearized by a C1 near-identity trans- formation of the form u = x+ \u03b1(x, y, z), v = y + \u03b2(x, y, z), w = z. (3.8) The proof of this result is given in three main steps: an invariant manifold theorem for a system with a spectral gap is used to find a preliminary near- identity C1 map, as in display (3.8), that transforms system (3.6) into a system of the same form but with the new function F = (f, g) \u201cflattened\u201d along the coordinate subspace corresponding to the invariant manifold. Equivalently, the identity D\u03b3(z)Cz \u2212A\u03b3(z) = F (\u03b3(z), z) (3.12) holds for all z in the domain of \u03b3.", "mime": "application/pdf"}, {"id": "ejde-401", "words": "2331", "extension": ".pdf", "flesch": "81", "author": "Peng, Peng; Wang, \u00a0Jinrong; O'Regan, Donal", "title": "Periodicity of non-homogeneous trajectories for non-instantaneous impulsive heat equations", "date": "2020", "keywords": "g(t", "summary": "[8] J. Wang, M. Fec\u030ckan; Non-instantaneous impulsive differential equations, IOP Publishing, 2018. For any s \u2208 I and t \u2208 R+, we have \u2016G(t, s)\u2016 \u2264 (\u03b2\u03b3)r(s,t), where \u03b2 = supi\u22651 supt\u2208(ti,si] \u2016Bi(t)\u2016 and \u03b3 = supi\u22651 \u2016E + Ii\u2016. Proof.", "mime": "application/pdf"}, {"id": "ejde-402", "words": "6202", "extension": ".pdf", "flesch": "79", "author": "Gasull, Armengol; Torregrosa, \u00a0Joan; Zhang, Xiang", "title": "Piecewise linear differential systems with an algebraic line of separation", "date": "2020", "keywords": "curve; cycles; differential; limit; linear; piecewise; system", "summary": "\u2212 y = 0. (3.4) \u2212 y = 0, (3.5) that passes trough the origin.", "mime": "application/pdf"}, {"id": "ejde-403", "words": "4484", "extension": ".pdf", "flesch": "79", "author": "Matveeva, Inessa I.", "title": "Exponential stability of solutions to nonlinear time-varying delay systems of neutral type equations with periodic coefficients", "date": "2020", "keywords": "y(t\u2212; y(t\u2212 \u03c4(t; \u03c4(t", "summary": "Taking into account that y(t) satisfies (1.1), we have d dt V (t, y) = \u2329 d dt H(t)y(t), y(t) \u232a + \u2329 H(t)z(t), y(t) \u232a + \u2329 H(t)F ( t, y(t), y(t\u2212 \u03c4(t)), d dt y(t\u2212 \u03c4(t)) ) , y(t) \u232a + \u2329 H(t)y(t), z(t) \u232a + \u2329 H(t)y(t), F ( t, y(t), y(t\u2212 \u03c4(t)), d dt y(t\u2212 \u03c4(t)) )\u232a + \u3008K(0)y(t), y(t)\u3009 \u2212 ( 1\u2212 d dt \u03c4(t) ) \u3008K(\u03c4(t))y(t\u2212 \u03c4(t)), y(t\u2212 \u03c4(t))\u3009 6 I. I. MATVEEVA EJDE-2020/20 + \u222b t t\u2212\u03c4(t) \u2329 d dt K(t\u2212 s)y(s), y(s) \u232a ds+ \u2329 L(0)z(t), z(t) \u232a + \u2329 L(0)F ( t, y(t), y(t\u2212 \u03c4(t)), EJDE-2020/20 EXPONENTIAL STABILITY OF SOLUTIONS 7 Consider the group of the summands containing F ( t, y(t), y(t \u2212 \u03c4(t)), ddty(t \u2212 \u03c4(t)) ) and denote them by W (t).", "mime": "application/pdf"}, {"id": "ejde-404", "words": "7037", "extension": ".pdf", "flesch": "79", "author": "Cuesta, Mabel; Leadi, Liamidi; Nshimirimana, Pascaline", "title": "Maximum and antimaximum principles for the p-Laplacian with weighted Steklov boundary conditions", "date": "2020", "keywords": "\u03bb1(m; \u03bb\u03021(m", "summary": "= e+ e\u22121 e\u2212 e\u22121 = \u03b2 = \u03bb\u03021(m). = \u2212 inf { \u2016u\u2016p1,p; I(u) = \u22121 and u \u2208 Q } , (4.2) where Q := { u \u2208W 1,p(\u2126);\u2203B(x0, r) s.t u|B(x0,r)\u2229\u2126 \u2261 0", "mime": "application/pdf"}, {"id": "ejde-407", "words": "9860", "extension": ".pdf", "flesch": "64", "author": "Jia, Jiwei; Ding, \u00a0Jian; Liu, Siyu; Liao, Guidong; Li, Jingzhi; Duan, Ben; Wang, Guoqing; Zhang, Ran", "title": "Modeling the control of COVID-19: impact of policy interventions and meteorological factors", "date": "2020", "keywords": "china; control; covid-19; data; days; disease; hubei; isolation; model; peak; period; province; sars; strategy; transmission", "summary": "For this reason alone, collecting massive data re- lating to COVID-19 and analyzing the inherent linkage among these data are of great importance for the next step of control strategy. Simulations for most provinces can conduce to understand the effect of control strategy in China.", "mime": "application/pdf"}, {"id": "ejde-408", "words": "3918", "extension": ".pdf", "flesch": "81", "author": "Geba, Dan-Andrei; Lin, Bai", "title": "Almost optimal local well-posedness for modified Boussinesq equations", "date": "2020", "keywords": "equation", "summary": "Fx, (2.1) where t \u2208 R is arbitrary, yet fixed. p\u220f j=1 \u2016(vj0, v j 1)\u2016Hs\u00d7Hs would hold uniformly for t \u2208", "mime": "application/pdf"}, {"id": "ejde-41", "words": "9267", "extension": ".pdf", "flesch": "88", "author": "Mo, Yichun; Zhu, Min; Feng, Binhua", "title": "Blow-up criteria and instability of standing waves for the fractional Schrodinger Poisson equation", "date": "2023", "keywords": "lemma; standing; waves", "summary": "C \u2212D = d(\u03c9), (4s+ 2r \u2212 3)A+ (2s+ 2r \u2212 3)B + (4s+ 2r \u2212 3)C \u2212 ((s+ r)(p+ 2)\u2212 3)D = 0, 2(\u00b5(4s+ 2r \u2212 3) + Then\u222b R3 (|x|\u2212(3\u22122r) \u2217 |un|2)|un|2dx = \u222b R3 (|x|\u2212(3\u22122r) \u2217 |un \u2212 u|2)|un \u2212 u|2dx + \u222b R3 (|x|\u2212(3\u22122r) \u2217 |u|2)|u|2dx+ \u25e6(1).", "mime": "application/pdf"}, {"id": "ejde-411", "words": "8639", "extension": ".pdf", "flesch": "84", "author": "dos Santos, Gelson C. G.; Figueiredo, Giovany M.; Tavares, \u00a0Leandro S.", "title": "Sub-super solution method for nonlocal systems involving the p(x)-Laplacian operator", "date": "2020", "keywords": "a(x; theorem", "summary": "Using Ho\u0308lder\u2019s inequality we have\u2223\u2223 \u222b \u2126 \u2329 |\u2207uin|pi(x)\u22122\u2207uin \u2212 |\u2207u|pi(x)\u22122\u2207ui,\u2207(uin \u2212 u) \u232a\u2223\u2223 \u2264 |uin Since \u03bbn \u2192 \u03bb and Hi(T1z 1 n, T2z 2 n)\u2192 Hi(T1z 1, T2z 2) in Lp \u2032 i(x)(\u2126) for i = 1, 2 we have\u2223\u2223 \u222b \u2126 \u2329 |\u2207uin|pi(x)\u22122\u2207uin \u2212 |\u2207u|pi(x)\u22122\u2207ui,\u2207(uin \u2212 u) \u232a\u2223\u2223\u2192 0.", "mime": "application/pdf"}, {"id": "ejde-412", "words": "6645", "extension": ".pdf", "flesch": "85", "author": "Louis-Rose, Carole", "title": "Null controllability from the exterior of fractional parabolic-elliptic coupled systems", "date": "2020", "keywords": "\u03bbn\u2212d", "summary": "Integrating over (0, 1)\u00d7 (0, T ), we obtain\u222b 1 0 \u222b T 0 (\u2202tu+ (\u2212d2 x)su)\u03d5dx dt = \u222b 1 0 \u222b T 0 (au+ bv)\u03d5dx dt,\u222b 1 0 \u222b T 0 \u03c3(\u2212d2 x)sv dx dt = \u222b 1 0 \u222b T 0 (cu+ dv)\u03c3 dx dt. \u222b 1 0 \u222b T 0 u\u2202t\u03d5dx dt + c1,s 2 \u222b R2 \u222b T 0 (u(x)\u2212 u(y))(\u03d5(x)\u2212 \u03d5(y)) |x\u2212 y|1+2s dx dy dt\u2212 \u222b R\\(0,1) \u222b T 0", "mime": "application/pdf"}, {"id": "ejde-413", "words": "7962", "extension": ".pdf", "flesch": "84", "author": "Zhang, Zhifei", "title": "Stabilization of the wave equation with variable coefficients and a dynamical boundary control", "date": "2020", "keywords": "conditions; equations; problem; solution; \u222b l; \u222b \u03c4", "summary": "dt = \u222b T 0 \u222b l 0 \u03b7(x, t) \u222b l 0 M(x, \u03be, t)u(\u03be, t)d\u03be dx dt + \u222b T 0 \u222b l 0 \u03b7(x, t)[S\u0303\u03be(x, 0, t)a(0, t)u(0, t)\u2212 S\u0303\u03be(x, l, t)a(l, t)u(l, t)] dt = \u222b T 0 \u222b l 0 \u03b7(x, t) \u222b l 0 M(x, \u03be, t)un\u22121(\u03be, t)d\u03be dx dt + \u222b T 0 \u222b l 0 \u03b7(x, t)[S\u0303\u03be(x, 0, t)a(0, t)un\u22121(0, t)\u2212 S\u0303\u03be(x, l, t)a(l, t)un\u22121(l, t)]", "mime": "application/pdf"}, {"id": "ejde-415", "words": "7962", "extension": ".pdf", "flesch": "84", "author": "Pulkina, Ludmila S.", "title": "Nonlocal problems for hyperbolic equations from the viewpoint of strongly regular boundary conditions", "date": "2020", "keywords": "conditions; equations; problem; solution; \u222b l; \u222b \u03c4", "summary": "dt = \u222b T 0 \u222b l 0 \u03b7(x, t) \u222b l 0 M(x, \u03be, t)u(\u03be, t)d\u03be dx dt + \u222b T 0 \u222b l 0 \u03b7(x, t)[S\u0303\u03be(x, 0, t)a(0, t)u(0, t)\u2212 S\u0303\u03be(x, l, t)a(l, t)u(l, t)] dt = \u222b T 0 \u222b l 0 \u03b7(x, t) \u222b l 0 M(x, \u03be, t)un\u22121(\u03be, t)d\u03be dx dt + \u222b T 0 \u222b l 0 \u03b7(x, t)[S\u0303\u03be(x, 0, t)a(0, t)un\u22121(0, t)\u2212 S\u0303\u03be(x, l, t)a(l, t)un\u22121(l, t)]", "mime": "application/pdf"}, {"id": "ejde-417", "words": "5721", "extension": ".pdf", "flesch": "84", "author": "Liang, Chen; Yan, Lixu; Fu, Yongqiang", "title": "Existence of solutions to stochastic p(t,x)-Laplace equations and applications", "date": "2024", "keywords": "stochastic", "summary": "L2dt\u2212 \u222b T 0 \u222b \u03a3 \u03b7\u2207\u03c6dxdt + \u222b T 0 \u27e8f(u(t)), \u03c6\u27e9(L2q(x))\u2217,L2q(x)dt+ \u222b T 0 (g(t), \u03c6)L2dt + \u222b T 0 (\u03c6, \u03c3dW (t))L2 . (2.2) The series converges strongly to \u222b T 0 \u03c3(s)dB(s) in LF 2 (\u2126, C([0, T ], O)).", "mime": "application/pdf"}, {"id": "ejde-418", "words": "10802", "extension": ".pdf", "flesch": "81", "author": "Sremr, Jiri", "title": "Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term", "date": "2023", "keywords": "problem; solution; t \u2208; theorem", "summary": "[6] X. Han, Y. He, H. Wei; Existence of positive periodic solutions for a nonlinear system of second-order ordinary differential equations, Electron. [14] J. S\u030cremr; Bifurcation of positive periodic solutions to non-autonomous undamped duffing equations, Math.", "mime": "application/pdf"}, {"id": "ejde-42", "words": "3977", "extension": ".pdf", "flesch": "77", "author": "Papageorgiou, Nikolaos S.; Vetro, Calogero; Vetro, Francesca", "title": "Positive solutions for singular (p,q)-Laplacian equations with negative perturbation", "date": "2023", "keywords": "1,p", "summary": "In (3.11) we use the test function h = u\u0303n \u2208 W 1,p 0 (\u2126). Introduction Let \u2126 \u2286 RN be a bounded domain with a C2-boundary \u2202\u2126. In this paper we study the following singular Dirichlet (p, q)-equation \u2212\u2206pu(z)\u2212\u2206qu(z)", "mime": "application/pdf"}, {"id": "ejde-421", "words": "5117", "extension": ".pdf", "flesch": "79", "author": "Brindle, Darin; N'Guerekata, Gaston M.", "title": "S-asymptotically omega-periodic mild solutions to fractional differential equations", "date": "2020", "keywords": "periodic", "summary": "= \u222b t 0 (t\u2212 s)\u03b1\u22122 \u0393(\u03b1\u2212 1) Au(s)ds+ f(t, u(t)), 1 < \u03b1 < 2, t \u2265 0 (2.1) u(0) = u0 + g(u) . Therefore, u\u2032(t) = \u222b t 0 (t\u2212 s)\u03b1\u22122 \u0393(\u03b1\u2212 1) Au(s)ds+ f(t, u(t)), 1 < \u03b1 < 2, t \u2265 0, (5.1) u(0) = u0 + g(u)", "mime": "application/pdf"}, {"id": "ejde-422", "words": "7970", "extension": ".pdf", "flesch": "79", "author": "Fan, Xiaoting; Wang, Shu; Xu, Wen-Qing", "title": "Initial-boundary layer associated with the 3-D Boussinesq system for Rayleigh-Benard convection", "date": "2020", "keywords": "b,0; boundary; t \u03b5", "summary": "= T 0 0 , (4.13) where the remainders are R\u03b5In,u = \u2212 \u221e\u2211 i=1 ( \u221a \u03b5)i(\u03b5[\u2202tu In,i + i\u2211 j=0 uIn,j \u00b7 \u2207uIn,i\u2212j ] +\u2207pIn,i + 1 Ek e3 \u00d7 uIn,i \u2212\u2206uIn,i \u2212Rae3T In,i), and R\u03b5In,T = \u2212 \u221e\u2211 i=1 ( \u221a \u03b5)i ( \u2202tT In,i + i\u2211 j=0 uIn,j \u00b7 \u2207T It follows from the divergence formula, divergence theorem, (4.46) and the bound- ary condition (4.48) that J5 = \u2212 \u222b X u\u03b5a \u00b7 \u2207 ( (T \u03b5e )2 2 ) dx dy dz = \u2212 \u222b X \u2207 \u00b7 ( u\u03b5a (T \u03b5e )2 2 )", "mime": "application/pdf"}, {"id": "ejde-423", "words": "4215", "extension": ".pdf", "flesch": "79", "author": "Tunc, Ercan; Grace, Said R.", "title": "Oscillatory behavior of solutions to third-order nonlinear differential equations with a superlinear neutral term", "date": "2020", "keywords": "differential; equations; order", "summary": "Oscillation of solutions; asymptotic behavior; neutral differential equation. [5] P. Das; Oscillation criteria for odd order neutral equations, J. Math.", "mime": "application/pdf"}, {"id": "ejde-424", "words": "4027", "extension": ".pdf", "flesch": "79", "author": "Tuan Duy, Nguyen; Long Phi, Le; Thanh Son, Nguyen", "title": "Hardy and Caffarelli-Kohn-Nirenberg inequalities with nonradial weights", "date": "2020", "keywords": "inequalities; nirenberg; rn\u2217", "summary": "Hardy inequality; Caffarelli-Kohn-Nirenberg inequality; monomial weight; radial derivation; best constant. [29] Lam, N.; A note on Hardy inequalities on homogeneous groups.", "mime": "application/pdf"}, {"id": "ejde-427", "words": "6106", "extension": ".pdf", "flesch": "73", "author": "Sun, Zhongyuan; Wang, Jinfeng", "title": "Dynamics and pattern formation in diffusive predator-prey models with predator-taxis", "date": "2020", "keywords": "predator; prey; taxis", "summary": "A reaction diffusion model with stage structure for the predator was proposed in [8], \u2202u \u2202t \u2212 d\u2206u = bv \u2212mu, x \u2208 \u2126, t > 0, \u2202v \u2202t \u2212 d\u2206v = ruw \u2212 v, x \u2208 \u2126, t > 0, \u2202w \u2202t \u2212 d1\u2206w = (a\u2212 w)w \u2212 \u03b5vw \u2212 uw, x \u2208 \u2126, t > 0, \u2202u \u2202\u03bd = \u2202v \u2202\u03bd = \u2202w \u2202\u03bd = 0, x \u2208 \u2202\u2126, u(x, 0) \u2265 0, v(x, 0) \u2265 0, w(x, 0) \u2265 0, x \u2208 \u2126, (1.1) where u(x, t), v(x, t) and w(x, t) represent the densities of mature predator, im- mature predator and prey respectively at position x and time t; \u2126 is a bounded domain in RN , N \u2265 1 with smooth boundary \u2202\u2126 and unit outer normal \u03bd; the ho- mogeneous Neumann boundary condition indicates that the predator-prey system is self-contained with zero population flux across the boundary. Predators are assumed to move randomly in their habitats, and prey mobiles to avoid the mature predators.", "mime": "application/pdf"}, {"id": "ejde-428", "words": "2551", "extension": ".pdf", "flesch": "74", "author": "Charro, Fernando", "title": "Explicit solutions of Jensen's auxiliary equations via extremal Lipschitz extensions", "date": "2020", "keywords": "lipschitz", "summary": "In this note we prove that McShane and Whitney\u2019s Lipschitz ex- tensions are viscosity solutions of Jensen\u2019s auxiliary equations which are known to have a key role in Jensen\u2019s celebrated proof of uniqueness of infinity har- monic functions, and therefore of absolutely minimizing Lipschitz extensions. Lipschitz extension; McShane-Whitney extension; infinity Laplacian.", "mime": "application/pdf"}, {"id": "ejde-429", "words": "9883", "extension": ".pdf", "flesch": "86", "author": "Cao, Feng; Gao, Lu", "title": "Transition fronts of two species competition lattice systems in random media", "date": "2020", "keywords": "lim; \u03b8t0\u03c9", "summary": "U(x+ \u222b t 0 c(s;\u03c9, \u00b5)ds, t;\u03c9) = u ( x+ \u222b T 0 c(s; \u03b8t\u2212T\u03c9, \u00b5)ds, T ;U(\u00b7+ \u222b t\u2212T 0 c(s;\u03c9, \u00b5)ds, t\u2212 T ;\u03c9), V (\u00b7+ \u222b t\u2212T 0 c(s;\u03c9, \u00b5)ds, t\u2212 T ;\u03c9), \u03b8t\u2212T\u03c9 ) > u\u2217(t;\u03c9)\u2212 2\u03b5, \u2200t \u2208 R, x \u2264 \u2212N, and hence limx\u2192\u2212\u221e U(x+ \u222b t 0 c(s;\u03c9, \u00b5)ds, t;\u03c9) = u\u2217(t;\u03c9) uniformly in t \u2208 R. Sim- ilarly, we can derive limx\u2192\u2212\u221e V (x + \u222b t 0 c(s;\u03c9, \u00b5)ds, t;\u03c9) = v\u2217(t;\u03c9) uniformly in t \u2208 R. a2(\u03b8t\u03c9)\u2212 2c2(\u03b8t\u03c9)v\u2217(t;\u03c9) + b2(\u03b8t\u03c9)v\u2217(t;\u03c9) for t \u2208 R. Under the assumptions (H1)\u2013(H3), one of the most interesting dynamical prob- lems is to study the existence of random transition front (generalized traveling wave) solutions connecting (u\u2217(t;\u03c9), 0) and (0, v\u2217(t;\u03c9)) for (1.1).", "mime": "application/pdf"}, {"id": "ejde-43", "words": "4536", "extension": ".pdf", "flesch": "78", "author": "Fereidooni, Amin; Moameni, Abbas; Grewal, Anant", "title": "Existence of solutions to steady Navier-Stokes equations via a minimax approach", "date": "2023", "keywords": "navier; stokes", "summary": "= \u2206v \u2212\u2207pv \u2200x \u2208 \u2126, in a weak sense; then there exists u\u0304 \u2208 K such that \u039bu\u0304+ f(x) Since v is the unique minimizer of I, we can conclude that v\u0304(x) = v(x); therefore, there exits v \u2208 K such that equation (3.2) is satisfied for a fixed u \u2208 K. Step 5: Note that the existence of v \u2208 K (as proved above) satisfies condition (i) of Theorem 1.1; therefore, a solution of the Navier-Stokes equations exist in the set K; i.e., there exists u\u0304 \u2208 K that satisfies the following equations: \u039bu\u0304+ f(x)", "mime": "application/pdf"}, {"id": "ejde-430", "words": "8164", "extension": ".pdf", "flesch": "87", "author": "Begout, Pascal", "title": "Finite time extinction for a damped nonlinear Schrodinger equation in the whole space", "date": "2020", "keywords": "be\u0301gout; l2(rn; solution", "summary": "By (4.17), (4.22), (4.23), Remark 2.9 and Ho\u0308lder\u2019s inequality (recalling that 2m < m+ 1 < 2), we obtain u \u2208 L\u221eloc ( [0,\u221e);H2(RN ) ) \u2229 L\u221eloc ( [0,\u221e);L2m(RN ) ) , (4.24) u \u2208 C ( [0,\u221e);L2(RN ) ) \u2229 L\u221eloc ( [0,\u221e);L2m(RN ) ) \u21aa\u2192 C ( [0,\u221e);Lm+1(RN ) ) . (4.25) Recalling that u \u2208 W 1,\u221e loc ( [0,\u221e);L2(RN ) ) , by (4.24) and the embedding 3) of Lemma A.4, we have u \u2208 C ( [0,\u221e);H1(RN ) ) .", "mime": "application/pdf"}, {"id": "ejde-431", "words": "7646", "extension": ".pdf", "flesch": "77", "author": "Ildefonso Diaz, Jesus; Padial, \u00a0Juan Francisco; Tello, Jose Ignacio; Tello, Lourdes", "title": "Complex Ginzburg-Landau equations with a delayed nonlocal perturbation", "date": "2020", "keywords": "solution", "summary": "(2.10) Then by Gronwall\u2019s lemma, we obtain that f(t) \u2264 K1 for t \u2208 (0, \u03c4). By integrating inequality (2.6) over (0, t), for t \u2208 (0, \u03c4) we obtain\u222b t 0 d dt \u2016u(s)\u20162L2(\u2126)ds \u2264", "mime": "application/pdf"}, {"id": "ejde-432", "words": "15989", "extension": ".pdf", "flesch": "76", "author": "Jimenez, Johana; Llibre, Jaume; Medrado, Joao C.", "title": "Crossing limit cycles for a class of piecewise linear differential centers separated by a conic", "date": "2020", "keywords": "centers; crossing limit; cycles; differential centers; limit cycles; linear differential; piecewise linear; points; system; theorem", "summary": "\u2212 b22(\u03bb2 + \u03bb3 \u2212 n2 \u2212 n3)\u03c81 + 2b2(\u2212\u03bb4\u03c82 +m2n2 \u2212m3n3) ) + k1 ( \u2212 \u03c82 + b22(\u03bb2 + \u03bb3 \u2212 n2 \u2212 n3)\u03c81 + 2b2(\u03bb1\u03c82 \u2212m2n2 +m3n3) )) + k2 ( (\u03bb1 \u2212 \u03bb4)(\u03c82 \u2212 b22(\u03bb1 + \u03bb4 \u2212 n2 \u2212 n3)\u03c81)\u2212 (k21 \u2212 k24)\u03c81 \u2212 2b2 ( \u03bb2(\u2212\u03bb4\u03c82 \u2212 (k1 \u2212 k4)\u03c81) + (\u03bb1 \u2212 \u03bb2)(\u03bb1 + \u03bb2 \u2212 \u03bb3 \u2212 l4)l1) ) , \u03b3 = 1 8(\u2212(k1 \u2212 k4)(\u03bb2 \u2212 \u03bb3) + (k2 \u2212 k3)(\u03bb1 \u2212 \u03bb4))", "mime": "application/pdf"}, {"id": "ejde-433", "words": "6264", "extension": ".pdf", "flesch": "87", "author": "Wang, Fei; Hao, Jianghao", "title": "Decay of energy for viscoelastic wave equations with Balakrishnan-Taylor damping and memories", "date": "2020", "keywords": "e(t; g1(t\u2212; \u2207u)(t; \u2212 \u222b; \u222b t; \u222b \u03c9; \u222b \u221e", "summary": "= 1 \u03c1+ 2 \u2016ut\u2016\u03c1+2 \u03c1+2 + 1 2 \u2016\u2207ut\u201622 + J(t), (2.10) where (g1 \u25e6 \u2207u)(t) = \u222b \u2126 a1(x) \u222b t 0 g1(t\u2212 s)|\u2207u(t)\u2212\u2207u(s)|2 ds dx, (g2 }\u2207u)(t) = \u222b \u2126 a2(x) \u222b \u221e 0 g2(s)|\u2207u(t)\u2212\u2207u(t\u2212 s)|2 ds dx. Lemma 2.3. E(t) is a non-increasing function for t \u2265 0, and E\u2032(t) = \u222b \u2126 a1(x) \u222b t 0 g\u20321(t\u2212 s)|\u2207u(t)\u2212\u2207u(s)|2 ds dx, (g\u20322 }\u2207u)(t)", "mime": "application/pdf"}, {"id": "ejde-434", "words": "4217", "extension": ".pdf", "flesch": "80", "author": "Li, Dandan; Du, Jiayin", "title": "\u00b5 pseudo rotating-periodic solutions for differential equations", "date": "2020", "keywords": "function; periodic; pseudo", "summary": "In this article, we combine rotating periodic functions with \u00b5 er- godic functions to obtain a new class of functions called \u00b5 pseudo rotating periodic functions. Recently, many researchers have studied rotating periodic functions and obtained a series of results; see [14, 15, 20, 22, 23, 24, 25].", "mime": "application/pdf"}, {"id": "ejde-435", "words": "6434", "extension": ".pdf", "flesch": "80", "author": "Meng, Fengjuan; Zhang, Fubao; Zhang, Yuanyuan", "title": "Multiple positive solutions for biharmonic equation of Kirchhoff type involving concave-convex nonlinearities", "date": "2020", "keywords": "lemma", "summary": "Note that \u3008I \u2032\u03bb(un), un\u3009=0 and \u3008I \u2032\u03bb(un), un\u3009 \u2212 \u3008I \u2032\u03bb(u), u\u3009 = \u3008I \u2032\u03bb(un)\u2212 I \u2032\u03bb(u), u\u3009 \u2212 \u3008I \u2032\u03bb(un), un \u2212 u\u3009 \u2192 0, as n\u2192\u221e, (2.12) we have \u3008I \u2032\u03bb(u), u\u3009 = 0, which implies u \u2208 N\u03bb. = \u3008I \u2032\u03bb(un)\u2212 I \u2032\u03bb(u), un \u2212 u\u3009 = \u2016un \u2212 u\u20162 + b \u222b RN |\u2207un|2dx \u222b RN |\u2207(un \u2212 u)|2dx \u2212 b (\u222b RN |\u2207u|2dx\u2212 \u222b RN |\u2207un|2dx )\u222b RN \u2207u\u2207(un \u2212 u)dx \u2212 \u03bb \u222b RN f1(x)(|un|q\u22122un \u2212 |u|q\u22122u)(un \u2212 u)dx \u2212 \u222b RN f2(x)(|un|p\u22122un \u2212 |u|p\u22122u)(un \u2212 u)dx = \u2016un \u2212 u\u20162 + b \u222b RN |\u2207un|2dx \u222b RN |\u2207(un \u2212 u)|2dx+ o(1)", "mime": "application/pdf"}, {"id": "ejde-438", "words": "6540", "extension": ".pdf", "flesch": "87", "author": "Su, Si; Zhang, Guo-Bao", "title": "Global stability of traveling waves for delay reaction-diffusion systems without quasi-monotonicity", "date": "2020", "keywords": "lim; system; t\u2208[0,1", "summary": "\u2016(u, v)\u2016 < r}, \u2202Kri = {u \u2208 Ki : \u2016u\u2016 = ri}, \u2202Pr = {(u, v) \u2208 P : \u2016(u, v)\u2016 = r}, Kri = {u \u2208 Ki : \u2016u\u2016 6 ri}, \u2200ri > 0, Pr = {(u, v) \u2208 P : u \u2208", "mime": "application/pdf"}, {"id": "ejde-44", "words": "12911", "extension": ".pdf", "flesch": "87", "author": "Bostan, Mihai", "title": "Periodic solutions for evolution equations", "date": "2002", "keywords": "existence; lim; periodic; solutions; t 0; x(t; \u2208 r", "summary": "|x0|+ \u222b T 0 |f(t)\u2212 g(t, x1)|dt (32) = |x0|+ \u222b T 0 |f(t)\u2212 g(t, x0)|dt, t \u2208 = \u222b T 0 f(t)dt, \u03c4 \u2208]0, T", "mime": "application/pdf"}, {"id": "ejde-441", "words": "7746", "extension": ".pdf", "flesch": "85", "author": "Su, Si; Zhang, Guo-Bao", "title": "Global stability of traveling waves for delay reaction-diffusion systems without quasi-monotonicity", "date": "2020", "keywords": "stability; waves", "summary": "\u2212 \u03b7, 0)d\u03b7 + \u222b t 0 e\u2212\u03b2(t\u2212s) \u222b \u221e \u2212\u221e G2(\u03b7, t\u2212 s) lim \u03be\u2192+\u221e P2(U10(\u03be \u2212 \u03b7 \u2212 c\u03c4, s\u2212 \u03c4)) d\u03b7 ds = e\u2212\u03b2tU20(\u221e, 0) \u222b \u221e \u2212\u221e G2(\u03b7, t)d\u03b7 + \u222b t 0 e\u2212\u03b2(t\u2212s)P2(U10(\u221e, s\u2212 \u03c4)) = e\u2212\u03b1t \u222b \u221e \u2212\u221e G1(\u03b7, t)U10(\u03be \u2212 \u03b7, 0)d\u03b7 + \u222b t 0 e\u2212\u03b1(t\u2212s) \u222b \u221e \u2212\u221e G1(\u03b7, t\u2212 s)P1(U20(\u03be \u2212 \u03b7 \u2212 c\u03c4, s\u2212 \u03c4)) d\u03b7 ds, U2(\u03be, t) = e\u2212\u03b2t \u222b \u221e \u2212\u221e G2(\u03b7, t)U20(\u03be \u2212 \u03b7, 0)d\u03b7 + \u222b t 0 e\u2212\u03b2(t\u2212s) \u222b \u221e \u2212\u221e G2(\u03b7, t\u2212 s)P2(U10(\u03be \u2212 \u03b7 \u2212 c\u03c4, s\u2212 \u03c4)) d\u03b7 ds (3.3) for t \u2208 [0, \u03c4 ], where Gi(\u03b7, t) is the heat kernel Gi(\u03b7, t)", "mime": "application/pdf"}, {"id": "ejde-442", "words": "3714", "extension": ".pdf", "flesch": "83", "author": "Lan, Yongyi; Tang, Biyun; Hu, Xian", "title": "Positive solutions of Schrodinger-Poisson systems with Hardy potential and indefinite nonlinearity", "date": "2020", "keywords": "h1(r3; schro\u0308dinger", "summary": "In this article, we study the nonlinear Schro\u0308dinger-Poisson system \u2212\u2206u+ u\u2212 \u00b5 u |x|2 + l(x)\u03c6u = k(x)|u|p\u22122u x \u2208 R3, \u2212\u2206\u03c6 = l(x)u2 x \u2208 R3, where k \u2208 C(R3) and 4 < p < 6, k changes sign in R3 and lim sup|x|\u2192\u221e k(x) More precisely, f(x, u) = k(x)|u|p\u22121u + \u00b5h(x)u, where 4 < p < 6 and \u00b5 > 0, k(x) \u2208 C(R3), k changes sign in R3, and lim|x|\u2192\u221e k(x)", "mime": "application/pdf"}, {"id": "ejde-446", "words": "9894", "extension": ".pdf", "flesch": "78", "author": "Llibre, Jaume; Pereira, Weber F.; Pessoa, Claudio", "title": "Phase portraits of Bernoulli quadratic polynomial differential systems", "date": "2020", "keywords": "node; phase; points; saddle; singular; system", "summary": "Now as e\u03b1 + f = e\u03b2 + f = 0 and \u03b1 6= \u03b2, we obtain e = 0. First we suppose that e\u03b1+f = 0, so the eigenvalues associated with singular points p1 = (\u03b1, 0) are \u03bb1 = 0 and \u00b51 = \u03b1\u2212\u03b2.", "mime": "application/pdf"}, {"id": "ejde-447", "words": "5141", "extension": ".pdf", "flesch": "80", "author": "Briozzo, Adriana C.", "title": "Supercooled Stefan problem with a Neumann type boundary condition", "date": "2020", "keywords": "boundary; solution", "summary": "Free boundary problems with diffusion coefficient given by (1.7) or with temper- ature dependent conductivity were considered in [2, 4, 6, 7, 16, 19, 23, 30]. Free boundary problems which involves the freezing of a supercooled liquid can be seen in [12, 13, 14, 17, 18, 22, 24].", "mime": "application/pdf"}, {"id": "ejde-448", "words": "8673", "extension": ".pdf", "flesch": "71", "author": "Calatayud, Julia; Caraballo, Tomas; Cortes, Juan Carlos; Jornet, Marc", "title": "Mathematical methods for the randomized non-autonomous Bertalanffy model", "date": "2020", "keywords": "density; process; solution; stochastic; theorem; x(t", "summary": "[t0, T ], \u03c9 \u2208 \u2126, x(t0, \u03c9) = x0(\u03c9), \u03c9 \u2208 \u2126. (1.1) In (1.1), we are also considering the stochastic processes a = {a(t, \u03c9) : t \u2208 [t0, T ], \u03c9 \u2208 \u2126}, b = {b(t, \u03c9) :", "mime": "application/pdf"}, {"id": "ejde-449", "words": "5298", "extension": ".pdf", "flesch": "82", "author": "Tao, Kai", "title": "Non-perturbative positivity and weak Holder continuity of Lyapunov exponent of analytic quasi-periodic Jacobi cocycles defined on a high dimension torus", "date": "2020", "keywords": "log", "summary": "There exists an N0 := N0(\u03bbv, a) such that for any N > N0, E \u2208 E , x2 \u2208 T and DN \u03c91, it holds meas { x1 \u2208 T : 1 N | N\u2211 j=1 Fixing x2, E \u2208 E and \u03bb > \u03bb0 with \u03ba = 1 100 , we expand uan into its Fourier series of x1 and denote the Fourier coefficient as u\u0302an(k, x2, E, \u03bb), i.e., uan(x,E, \u03bb) = \u2211 k\u2208Z u\u0302an(k, x2, E, \u03bb)e2\u03c0ikx1 , u\u0302an(k, x2, E, \u03bb) = \u222b x1\u2208T uan(x1, x2, E, \u03bb)e\u22122\u03c0ikx1dx1.", "mime": "application/pdf"}, {"id": "ejde-45", "words": "31013", "extension": ".pdf", "flesch": "80", "author": "Escobedo, Miguel; Mischler, Stephane; Valle, Manuel A.", "title": "Homogeneous Boltzmann equation in quantum relativistic kinetic theory", "date": "2003", "keywords": "= \u222b; boltzmann; boltzmann equation; bose; case; collision; cross; ejde\u20132003; entropy; equation; escobedo; e\u2212\u03b5\u2032; fermi; function; mischler; mon; non; particles; problem; q(f; quantum; section; \u2212 \u222b; \u222b r3; \u222b \u221e; \u222b \u222b", "summary": "= \u222b \u221e 0 [(1 + F ) ln(1 + F )\u2212 F lnF \u2212 \u03b5F ]\u03b52d\u03b5. (4.52) = \u222b R3 ( (1 + F ) ln(1 + F )\u2212 F lnF \u2212 F\u03b20E1(p) ) dp (4.21) and DBQ(F )", "mime": "application/pdf"}, {"id": "ejde-452", "words": "8139", "extension": ".pdf", "flesch": "81", "author": "Wang, Xiaohui; Zhao, Peihao", "title": "Existence of weak solutions to superlinear elliptic systems without the Ambrosetti-Rabinowitz condition", "date": "2020", "keywords": "condition; lim; superlinear", "summary": "We first consider the p-Laplacian equation \u2212\u2206pu = \u03bbf(x, u) in \u2126, u = 0 on \u2202\u2126, (1.1) where p > 1, \u03bb > 0, \u2126 \u2282 Rn is a bounded domain, f : \u2126 \u00d7 R \u2192 R is a continuous function, and for 1 < p <\u221e, the p-Laplacian operator is \u2206pu = div(|Du|p\u22122Du) for u \u2208W 1,p(\u2126). |t|p = +\u221e a.e. in \u2126, or lim t\u2192\u2212\u221e F (x, t) |t|p = +\u221e a.e. in \u2126. Our first objective is to establish the existence of the nontrivial weak solution for the p-Laplacian superlinear elliptic equation (1.1) under the weaker condition than the AR condition in this paper.", "mime": "application/pdf"}, {"id": "ejde-453", "words": "8402", "extension": ".pdf", "flesch": "81", "author": "Salako, Rachidi B.; Shen, Wenxian", "title": "Traveling wave solutions for fully parabolic Keller-Segel chemotaxis systems with a logistic source", "date": "2020", "keywords": "wave", "summary": "= c in the interval (0,min{ \u221a a, \u221a \u03bb+\u03c4a (1\u2212\u03c4)+ }). Parabolic chemotaxis system; logistic source; traveling wave solution; minimal wave speed.", "mime": "application/pdf"}, {"id": "ejde-456", "words": "5794", "extension": ".pdf", "flesch": "80", "author": "Riva, Lorenzo; Pennington, Nathan", "title": "Low regularity of non-L^2(R^n) local solutions to gMHD-alpha systems", "date": "2020", "keywords": "sup; \u03b3\u22123", "summary": "\ufe38 \ufe37\ufe37 \ufe38 RHS of (3.4) = \u03b3\u22123 \u2212 r0 + n p0 \u2212 n p1 \u2265 0, the list reduces to \u03b3\u22123 \u2212 1 \u2264 r0 \u2264 \u03b3\u22123 \u2264 r1, r0 < n p1 , \u03b3\u22121 > 1\u2212 2r0 + r1 + 2n p0 \u2212 n p1 . 3.3. With this new bound on W1(u, v), we come back to J1 and see that J1 \u2264 sup (0,T ) \u222b t 0 (t\u2212 s)\u2212(r0\u2212(\u03b3\u22123 \u22121)+n/\u03c01\u2212n/p0)/\u03b3\u22121 \u2016W1(u, v)\u2016\u03b3\u22123 \u22121,\u03c01 ds \u2264 C sup (0,T ) \u222b t 0 (t\u2212 s)\u2212(r0\u2212(\u03b3\u22123 \u22121)+n/\u03c01\u2212n/p0)/\u03b3\u22121 \u2016u\u2016r0,p0\u2016u\u2016r1,p1ds = C sup (0,T ) \u222b t 0 (t\u2212 s)\u2212(r0\u2212(\u03b3\u22123 \u22121)+n/\u03c01\u2212n/p0)/\u03b3\u22121 s\u2212a1\u2016u\u2016r0,p0sa1\u2016u\u2016r1,p1ds \u2264 C\u2016u\u20160;r0,p0\u2016u\u2016a1;r1,p1 sup (0,T ) \u222b t 0 (t\u2212 s)\u2212(r0\u2212(\u03b3\u22123 \u22121)+n/\u03c01\u2212n/p0)/\u03b3\u22121 s\u2212a1ds < CM2T 1\u2212(r0\u2212(\u03b3\u22123 \u22121)+n/\u03c01\u2212n/p0)/\u03b3\u22121 \u2212a1 , where the last inequality holds by Proposition 2.3, if \u03b3\u22121 > r0 \u2212 (\u03b3\u22123 \u2212 1) + n \u03c01 \u2212 n p0 + \u03b31a1 = r0 \u2212 (\u03b3\u22123 \u2212 1) + n ( 1 p0 + 1 p1 \u2212 r0 n )", "mime": "application/pdf"}, {"id": "ejde-457", "words": "8682", "extension": ".pdf", "flesch": "72", "author": "Oliveira, Regilene; Valls, Claudia", "title": "Global dynamics of the May-Leonard system with a Darboux invariant", "date": "2020", "keywords": "orbits; system", "summary": "Moreover, the f1(x, y, z) = 0, f2(x, y, z) = 0 and f3(x, y, z) = 0 have cofactors, 1 \u2212 x \u2212 \u03b1y \u2212 \u03b2z, 1 \u2212 \u03b2x \u2212 y \u2212 \u03b1z and 1 \u2212 \u03b1x \u2212 \u03b2y \u2212 z, respectively. Denote by X\u0304 the vector field D(f \u25e6 X) defined on S2 \\ S1, where S1 = {y \u2208 S2 : y3 = 0} is identified with the infinity of R2.", "mime": "application/pdf"}, {"id": "ejde-458", "words": "6481", "extension": ".pdf", "flesch": "88", "author": "Li, Guofa; Cheng, Bitao; Huang, Yisheng", "title": "Positive solutions for asymptotically 3-linear quasilinear Schrodinger equations", "date": "2020", "keywords": "h1(rn; lemma; rn v; \u222b rn", "summary": "(3) Given y \u2208 RN and setting uy(x) := u(x\u2212 y), we have \u03b2(uy) = \u03b2(u) + y. Lemma 4.10. = \u222b t 0 h(s)ds.", "mime": "application/pdf"}, {"id": "ejde-459", "words": "7017", "extension": ".pdf", "flesch": "74", "author": "Barreira, Luis; Llibre, Jaume; Valls, Claudia", "title": "Linear type global centers of cubic Hamiltonian systems symmetric with respect to the x-axis", "date": "2020", "keywords": "linear; origin; points; singular", "summary": "Thus on the local chart U2 we obtain u\u2032 = \u22123a12uv \u2212 3a30u 3v \u2212 cu2v2 \u2212 \u03b1u4 \u2212 \u03c92 c v2, v\u2032 = \u2212v(a12v \u2212 a21x2 \u2212 2a12xy \u2212 3a03y 3 \u2212 3\u03b1\u00b5x2y \u2212 \u03b1y3, y\u0307 = cx+ dy + 3a30x 2 + 2a21xy + a12y 2 + 3\u03b1\u00b5xy2. 6 L. BARREIRA, J. LLIBRE, C. VALLS EJDE-2020/57 Since this system must be invariant under the transformation (x, y, t) 7\u2192 (x,\u2212y,\u2212t) we must have d = a21 = a03 = 0", "mime": "application/pdf"}, {"id": "ejde-46", "words": "57992", "extension": ".pdf", "flesch": "93", "author": "Wang, Hwai-chiuan", "title": "Palais-Smale approaches to semilinear elliptic equations in unbounded domains", "date": "2004", "keywords": "approaches; ar 0; chiuan; domain; domain \u03c9; ejde-2004; equation; exists; following; h1 0; hwai; iii; jh(u0; lemma; lim; mon; o(1; palais; proof; sequence; smale; solution; state; subsequence; symmetric; t \u2208; theorem; u \u2208; u(x; wang; x(\u03c9; z \u2208; \u03b1(ar; \u2208 ar; \u2208 h1; \u2208 r; \u2212 \u222b; \u222b \u03c9", "summary": "Then for r > 0, x \u2208 \u2126 exists such that B\u0303N (x, r) \u2282 \u2126\u0303, which means that for any y\u0303 \u2208 B\u0303N (x, r), y \u2208 \u2126 exists and y\u0303 is the projection of y. By Lemma 10.9, \u03bb > 0 exists such that {y\u0303 \u2212 \u03c7t : t \u2265 \u03bb} \u2282 p |x\u2212 y|\u03b8 a.e. for x, y \u2208 \u2126 and |\u03b2| = k. In particular, Wm,p(\u2126) \u21aa\u2192 Ck,\u03b8(\u2126).", "mime": "application/pdf"}, {"id": "ejde-460", "words": "6402", "extension": ".pdf", "flesch": "80", "author": "He, Ze-Rong; Zhou, Nan", "title": "Controllability and stabilization of a nonlinear hierarchical age-structured competing system", "date": "2020", "keywords": "system; \u2212 \u222b", "summary": "\u2202t = \u2212\u03b1 \u222b t 0 bui i (\u03c4)Mi(t\u2212 \u03c4, t) exp { \u2212 \u222b t \u03c4 Mi(v \u2212 \u03c4, v)dv } d\u03c4 + \u03b1bui i (t)\u2212 \u03b1p0i (a\u2212 t) exp { \u2212 \u222b t 0 Mi(a\u2212 t+ \u03c4, \u03c4)d\u03c4 } \u2212 \u03b1 \u222b a\u2212t 0 p0i (v)Mi(v + t, t) exp { \u2212 \u222b t 0 Mi(v + \u03c4, \u03c4)d\u03c4 } dv \u2212 p0i (A\u2212 t) exp { \u2212 \u222b t 0 Mi(A\u2212 t+ \u03c4, \u03c4)d\u03c4 } + p0i (a\u2212 t) exp { \u2212 \u222b t 0 Mi(a\u2212 t+ \u03c4, \u03c4)d\u03c4 } \u2212 \u222b A\u2212t a\u2212t p0(v)Mi(v + t, t) exp { \u2212 \u222b t 0 Mi(v + \u03c4, \u03c4)d\u03c4 } dv + \u03b1 \u222b t 0 exp { \u2212 \u222b t v Mi(\u03b8 \u2212 t, \u03b8)d\u03b8 } ui(v \u2212 t, v)dv \u2212 \u03b1 \u222b t 0 \u222b s 0 Mi(t\u2212 s, t) exp { \u2212 \u222b t v Mi(\u03b8 \u2212 s, \u03b8)d\u03b8 } ui(v \u2212 s, v)dvds \u2212 \u03b1 \u222b t 0 exp { \u2212 \u222b t v Mi(\u03b8 + a\u2212 t, \u03b8)d\u03b8 } ui(v + a\u2212 t, v)dv + \u03b1 \u222b a\u2212t 0 [ui(t+ s, t) \u2212 \u222b t 0 ui(v + s, s)Mi(t+ s, t) exp { \u2212 \u222b t v Mi(\u03b8 + s, \u03b8)d\u03b8 } ]ds \u2212 \u222b t 0 exp { \u2212 \u222b t v Mi(\u03b8 +A\u2212 t, \u03b8)d\u03b8 } ui(v +A\u2212 t, v)dv + \u222b t 0 exp { \u2212 \u222b t v Mi(\u03b8 + a\u2212 t, \u03b8)d\u03b8 } ui(v + a\u2212 t, v)dv EJDE-2020/58 CONTROLLABILITY OF HIERARCHICAL SYSTEMS 7 + \u222b A\u2212t a\u2212t + \u222b t 0 Ki(t, s;P )bui i (t\u2212 s;P )ds, t \u2208 (0, T ), (3.7) EJDE-2020/58 CONTROLLABILITY OF HIERARCHICAL SYSTEMS 5 where Fi(t;P )", "mime": "application/pdf"}, {"id": "ejde-461", "words": "11812", "extension": ".pdf", "flesch": "69", "author": "Floridia, Giuseppe", "title": "Nonnegative controllability for a class of nonlinear degenerate parabolic equations with application to climate science", "date": "2020", "keywords": "a(\u22121; case; controllability; equations; function; l2(\u22121; proposition; solution; t t1", "summary": "Integrating by parts, recalling that u\u2212(\u00b7, t) \u2208 H1 a(\u22121, 1) for every t \u2208 (0, T ),and using Proposition 3.1 we deduce\u222b 1 \u22121 (a(x)ux)xu \u2212 dx = [a(x)uxu \u2212]1\u22121 \u2212 \u222b 1 \u22121 a(x)ux(u\u2212)x dx = [a(x)uxu \u2212]1\u22121 + \u222b 1 \u22121 a(x)u2x dx . (3.2) If \u03b21\u03b31 6= 0, keeping in mind the boundary conditions, for t \u2208 (0, T ) we have [a(x)uxu \u2212]1\u22121 = a(1)ux(1, t)u\u2212(1, t)\u2212 a(\u22121)ux(\u22121, t)u\u2212(\u22121, t) = \u2212\u03b30 \u03b31 (u+(1, t)\u2212 u\u2212(1, t))u\u2212(1, t) For a.e. x \u2208 (\u22121, 1), from the equation ut(\u00b7, t) = \u03b1\u03b5j(\u00b7) T \u2212 T1 u(\u00b7, t) + ((a(\u00b7)ux(\u00b7, t))x + f(\u00b7, t, u)) t \u2208 (T1, T ), by the classical variation constants technique, we obtain a representation formula of the solution u(x, t) of (3.24), that computed at time T , for x \u2208 (\u22121, 1), becomes u(x, T )", "mime": "application/pdf"}, {"id": "ejde-465", "words": "6380", "extension": ".pdf", "flesch": "79", "author": "Huang, Chuangxia; Wang, Jiafu; Huang, Lihong", "title": "Asymptotically almost periodicity of delayed Nicholson-type system involving patch structure", "date": "2020", "keywords": "j=1; j=1,j; lim", "summary": "Obviously, according to the biological interpretation of Nicholson\u2019s blowflies models in [22, 17], it is necessary to relax the above technical conditions as follows: M lim sup t\u2192+\u221e \u03b3ij(t) \u2264 \u03ba\u0303, for all i \u2208 Q, j \u2208 I, (1.8) sup t\u2208[t0,+\u221e) {\u2212aii(t) + n\u2211 j=1,j 6=i aij(t) + 1 eM m\u2211 j=1 \u03b2ij(t) \u03b3ij(t) } < 0, i \u2208 Q, (1.9) lim inf t\u2192+\u221e {\u2212aii(t) + n\u2211 j=1,j 6=i aij(t) + m\u2211 j=1 \u03b2ij(t) \u03b3ij(t) e\u2212\u03ba} > 0, i \u2208 Q. (1.10) \u03c4hi0j(t))e \u2212\u03b3h i0j(t)xi0 (t\u2212\u03c4h i0j(t)), for t \u2208 [t0, t\u0304i0), we obtain 0", "mime": "application/pdf"}, {"id": "ejde-467", "words": "13306", "extension": ".pdf", "flesch": "67", "author": "Ivorra, Benjamin; Ngom, Diene; Ramos, Angel M.", "title": "Stability and sensitivity analysis of the epidemiological model Be-CoDiS predicting the spread of human diseases between countries", "date": "2020", "keywords": "countries; country; day\u22121; disease; epidemic; equilibrium; model; parameters; people; rate; state; system; time", "summary": "[34] Z. Shuai, P. Van den Driessche; Global stability of infectious disease models using lyapunov functions, SIAM Journal on Applied Mathematics 73 (2013), no. 4, 1513\u20131532. Here, we have considered the functions (see [27]): mI,i(t) = mH,i(t) = mD,i(t) = exp ( \u2212 \u03bai max(t\u2212 \u03bbi, 0) ) , (2.2) where \u03bai in [0,+\u221e) (day\u22121) simulates the efficiency of the control mea- sures (greater value implies lower value of disease contact rates) and \u03bbi in R \u222a {+\u221e} (day) denotes the first day of application of those control mea- sures.", "mime": "application/pdf"}, {"id": "ejde-469", "words": "9601", "extension": ".pdf", "flesch": "82", "author": "Benes, Michal", "title": "Global weak solutions to degenerate coupled transport processes in partially saturated deformable elastic-inelastic porous media", "date": "2020", "keywords": "n n; \u03d1n\u22121", "summary": "In (1.1)\u2013(1.9), p : \u2126T \u2192 R, \u03d1 : \u2126T \u2192 R, \u03c3 : \u2126T \u2192 R4, \u03b5p` : \u2126T \u2192 R4 and \u03b1 : \u2126T \u2192 Rd, d \u2208 N, are the unknown functions. [L2(\u2126)]4 and \u03b1n\u22121 N \u2208 [L2(\u2126)]d, n = 1, . .", "mime": "application/pdf"}, {"id": "ejde-47", "words": "85791", "extension": ".pdf", "flesch": "87", "author": "Squassina, Marco", "title": "Existence, multiplicity, perturbation, and concentration results for a class of quasi-linear elliptic problems", "date": "2006", "keywords": "+ \u221e; + \u221e.; 1,p; a.e; c \u2208; case; class; condition; dsl; ejde-2006; equations; existence; f(u; following; function; h dx; h \u222b; j=1 \u222b; js(x; lemma; lim; linear; marco; mon; p \u222b; palais; point; problems; proof; results; s \u2208; satisfies; sequence; smale; solution; squassina; sup; t \u2208; that\u222b \u03c9; theorem; u dx; u k; u \u2208; u,\u2207u; uh,\u2207uh; x \u2208; \u03bd \u222b; \u03be \u2208; \u03c9 aij(x; \u03c9 b; \u03c9 g(x; \u03c9 j\u03be(x; \u03c9 l\u221e(x,\u2207u; \u03c9 n\u2211; \u03c9 |u+; \u03c9 \u03c6p\u22121; \u03c9 \u03d5; \u03c9 \u2207\u03bel; \u03d5 \u2208; \u2192 +; \u2208 h1; \u2208 l1(\u03c9; \u2208 r; \u2212 n\u2211; \u2212 \u222b; \u222b rn; \u222b \u03c9; \u2264 \u222b; \u2265 \u222b", "summary": "ON A CLASS OF QUASI-LINEAR ELLIPTIC PROBLEMS 143 \u00b5j \u2265 S\u03c3 p p\u2217 j , (6.111) where \u03b4xj denotes the Dirac measure at xj \u2208 \u2126 and S denotes the best Sobolev constant for the embedding W 1,p 0 (\u2126) \u21aa\u2192 Lp \u2217 (\u2126) (see e.g. [138]). Let x0 \u2208 \u2126 and \u03b4 > 0 and consider the functions T\u03b4,x0 as in (6.113).", "mime": "application/pdf"}, {"id": "ejde-470", "words": "5804", "extension": ".pdf", "flesch": "68", "author": "Castilho, Cesar; Gondim, Joao A. M.; Marchesin, Marcelo; Sabeti, Mehran", "title": "Assessing the efficiency of different control strategies for the COVID-19 epidemic", "date": "2020", "keywords": "age; class; control; epidemic; figure; model; number; parameters; quarantine; seir; strategies", "summary": "The second one evaluates different quarantine strategies by comparing their relative total number of deaths. In Section 5, different quarantine strategies for different age classes are considered and compared.", "mime": "application/pdf"}, {"id": "ejde-471", "words": "7654", "extension": ".pdf", "flesch": "79", "author": "Soriano Hernandez, Lorena; Siciliano, Gaetano", "title": "Existence and asymptotic behavior of solutions to eigenvalue problems for Schrodinger-Bopp-Podolsky equations", "date": "2023", "keywords": "solutions; theorem", "summary": "We study the existence and multiplicity of solutions for the Schro\u0308dinger-Bopp-Podolsky system \u2212\u2206u+ \u03c6u = \u03c9u in \u2126 a2\u22062\u03c6\u2212\u2206\u03c6 = u2 in \u2126 u = \u03c6 = \u2206\u03c6 = 0 on \u2202\u2126\u222b \u2126 u2 dx = 1 where \u2126 is an open bounded and smooth domain in R3, a > 0 is the Bopp- Podolsky parameter. \u00d7 H is a weak solution of (1.1) if\u222b \u2126 \u2207ua\u2207v dx+ \u222b \u2126 \u03c6auav dx = \u03c9a \u222b \u2126 uav dx for all v \u2208 H1 0 (\u2126) (1.2) and a2 \u222b \u2126 \u2206\u03c6a\u2206v dx+ \u222b \u2126 \u2207\u03c6a\u2207v dx", "mime": "application/pdf"}, {"id": "ejde-472", "words": "6213", "extension": ".pdf", "flesch": "72", "author": "Wang, Guiyun; Zheng, Shenzhou", "title": "Boundedness on generalized Morrey spaces for the Schrodinger operator with potential in a reverse Holder class", "date": "2023", "keywords": "morrey; spaces", "summary": "Schro\u0308dinger operators; reverse Ho\u0308lder class; generalized Morrey space; vanishing generalized Morrey space; BMO\u03b8(\u03c1) coefficients. This is done in in generalized Morrey spaces, and in vanishing generalized Morrey spaces.", "mime": "application/pdf"}, {"id": "ejde-475", "words": "11008", "extension": ".pdf", "flesch": "87", "author": "Besalu, Mireia; Binotto, Giulia; Rovira, Carles", "title": "Convergence of delay equations driven by a Holder continuous function of order 1/3", "date": "2020", "keywords": "b)(\u03c3; sup; t s; \u03b2\u2032(a", "summary": "t | \u2264 N\u2206\u0303\u03b2 y \u2264 T \u2206\u0303\u03b2\u22121 y + \u2206\u0303\u03b2 y . (5.42) 18 M. BESALU\u0301, G. BINOTTO, C. ROVIRA EJDE-2020/65 By Proposition 4.2 we have A2 \u2264 K\u2016\u03c3\u2016\u221e \u03a6\u03b2\u2032(a,b)(y \u2212 y\u00b7\u2212r, y) +K ( \u2016\u03c3\u2032\u2016\u221e + \u2016\u03c3\u2032\u2016\u03bb\u2016x\u0302r\u2016\u03bb\u03b2\u2032(a,b)T \u03bb\u03b2\u2032 ) \u03a6\u03b2\u2032(a,b)(x\u0302 r, y \u2212 y\u00b7\u2212r, y)T \u03b2 \u2032 = K\u2016y\u2016\u03b2\u2032 ( \u2016\u03c3\u2016\u221e + ( \u2016\u03c3\u2032\u2016\u221e + \u2016\u03c3\u2032\u2016\u03bb\u2016x\u0302r\u2016\u03bb\u03b2\u2032T\u03bb\u03b2 \u2032 )", "mime": "application/pdf"}, {"id": "ejde-476", "words": "7999", "extension": ".pdf", "flesch": "83", "author": "Gialelis, Nikolaos", "title": "Inviscid limit of linearly damped and forced nonlinear Schrodinger equations", "date": "2020", "keywords": "0,2,u; equations", "summary": "[0, T ]\u00d7 U, (1.1) where \u03bb \u2208 R\u2217 and \u03b1 > 0, \u03b3 > 0 and u = u(t, x; \u03b3), f = f(t, x; \u03b3) are complex-valued functions for t \u2208 [0, T ], then, following the notation of, e.g., [11] and [23], we associate with u the mapping u : [0, T ] \u2192 F(U ;C), defined by [u(t)](x) := u(t, x), for every x \u2208 U and t \u2208", "mime": "application/pdf"}, {"id": "ejde-48", "words": "31094", "extension": ".pdf", "flesch": "79", "author": "Gorban, Alexander N.", "title": "Singularities of transition processes in dynamical systems: Qualitative theory of critical delays", "date": "2004", "keywords": "limit; motion; point; proof; proposition; relaxations; sequence; set; sets; slow; system; theorem; \u03c9(x", "summary": "For a given parameter value k \u2208 K and an initial state x \u2208 X, the \u03c9-limit set \u03c9(x, k) is the set of all limit points of f(t, x, k) as t\u2192\u221e: y is in \u03c9(x, k) if and only if there exists a sequence ti \u2265 0 such that ti \u2192\u221e and f(ti, x, k) \u2192 y. Examples of \u03c9-limit points are stationary (fixed) points, points of limit cycles and so on. [0,\u221e)\u00d7X \u00d7K \u2192 X (1.1) be a continuous mapping for any t \u2265 0, k \u2208 K; let mapping f(t, \u00b7, k) : X \u2192 X be homeomorphism of X into subset of X and under every k \u2208 K let these homeomorphisms form monoparametric semigroup: f(0, \u00b7, k)", "mime": "application/pdf"}, {"id": "ejde-480", "words": "3425", "extension": ".pdf", "flesch": "85", "author": "Nguyen, Tu", "title": "Lower bounds at infinity for solutions to second order elliptic equations", "date": "2023", "keywords": "|x|", "summary": "They proved that if u satisfies (1.1) then there exists C > 0 such that\u222b B(x,1) u2 \u2265 exp(\u2212C|x|4/3 log |x|) \u2200|x| \u2265 10. Then there exists C2 > 0 such that if |x| = R \u2265 10, then\u222b B(x,\u03c4R) u2 \u2265 e\u2212C2R \u03b1 (3.4) and \u222b B(x,1) u2 \u2265 e\u2212C2R \u03b1 logR. (3.5) Proof.", "mime": "application/pdf"}, {"id": "ejde-482", "words": "11252", "extension": ".pdf", "flesch": "77", "author": "Zhang, Xuping; Chen, Pengyu; Li, Yongxiang", "title": "Monotone iterative method for retarded evolution equations involving nonlocal and impulsive conditions", "date": "2020", "keywords": "banach; equations; function; solution; v(0; w(0", "summary": "We mention that in 2012, Chuong and Ke [18] studied the retarded evolution inclusions involving nonlocal and impulsive conditions u\u2032(t) +Au(t) \u2208 F (t, u(t), ut), t \u2208 If a function u \u2208 PC([\u2212r, a], X) \u2229 C1(I \u2032\u2032, X) \u2229 C(I \u2032, X1) satisfies u\u2032(t) +Au(t) \u2264 f(t, u(t), ut), t \u2208", "mime": "application/pdf"}, {"id": "ejde-483", "words": "7340", "extension": ".pdf", "flesch": "84", "author": "Danecek, Josef; Viszus, Eugen", "title": "Holder continuity for vector-valued minimizers of quadratic functionals", "date": "2020", "keywords": "a\u03b1\u03b2ij", "summary": "Case A\u03b1\u03b2ij = A\u03b1\u03b2ij (u). Case A\u03b1\u03b2ij = A\u03b1\u03b2ij (x, u).", "mime": "application/pdf"}, {"id": "ejde-484", "words": "9173", "extension": ".pdf", "flesch": "67", "author": "Mushayabasa, Steady; Losio, Anthony A. E.; Modnak, Chairat; Wang, Jin", "title": "Optimal control analysis applied to a two-patch model for Guinea worm disease", "date": "2020", "keywords": "control; disease; e\u2217i; model; number; patch; total; worm", "summary": "In particular we will investigate heterogeneity on (i) disease transmission rates, with the assumption that \u03b22 = 6\u03b21 (ii) bounds of the controls a2 < a1 (iii) both disease transmission rates and upper bounds of the controls. As we can observe, an increase in disease transmission rate for the risk patch (patch 2) will lead to an increase on the total number of new infections and total cost over a period of 120 months.", "mime": "application/pdf"}, {"id": "ejde-486", "words": "6816", "extension": ".pdf", "flesch": "82", "author": "Zhao, Yihan; Xia, Yuanpei; Yang, Zhichun", "title": "Asymptotic behavior of stochastic three-species predator-prey systems with white and Levy noise", "date": "2020", "keywords": "stochastic; system; \u2212r2", "summary": "= (r1 \u2212 \u03b21 \u2212 a11eu1(t) Combining inequality (3.5), (3.2) and Lemma 2.6, we can deduce that a22x2(t)\u2217 \u2265 lim inf t\u2192\u221e { \u2212 r2 \u2212 \u03b22 \u2212 ln(x2(t)/x2(0))", "mime": "application/pdf"}, {"id": "ejde-487", "words": "7335", "extension": ".pdf", "flesch": "85", "author": "Qiu, Kee; Wang, Jinrong", "title": "Representation of solutions of a second order delay differential equation", "date": "2020", "keywords": "a(x\u2212; \u03b3(1", "summary": "\u222b 0 \u2212\u03c41 V (x\u2212 2\u03c41 \u2212 s)\u03c6(s)(ds)\u03b1 + A2B2 \u0393(1 + \u03b1) \u222b 0 \u2212\u03c41 V (x\u2212 \u03c41 \u2212 \u03c42 \u2212 s)\u03c6(s)(ds)\u03b1 + A2B2 \u0393(1 + \u03b1) \u222b 0 \u2212\u03c42 V (x\u2212 \u03c41 \u2212 \u03c42 \u2212 s)\u03c6(s)(ds)\u03b1 + B4 \u0393(1 + \u03b1) \u222b 0 \u2212\u03c42 V (x\u2212 2\u03c42 \u2212 s)\u03c6(s)(ds)\u03b1 \u2212 A2 \u0393(1 + \u03b1) \u222b", "mime": "application/pdf"}, {"id": "ejde-488", "words": "7004", "extension": ".pdf", "flesch": "62", "author": "Fama, Alessio; Restuccia, Liliana", "title": "Propagation of coupled porosity and fluid-concentration waves in isotropic porous media", "date": "2020", "keywords": "concentration; equations; field; fluid; flux; isotropic; porosity; propagation; tensor; waves", "summary": "= C1 = L1 = L2, D2 = B3 = C2 = L3, D3 = B4 = B5 = C3 = C5 = L4 = L5 = L7 = L10, D4 = B6 = C4 = C8 = L6 = L13, D5 = B7 = C6 = L8 = L11, D6 = B8 = B9 = C7 = C9 = L9 = L12 = L14 = L15, (5.18) where we have used expressions (5.13) and (5.16). +B4(\u03b4ik\u03b4jl + \u03b4il\u03b4jk)\u03b4mn +B5(\u03b4ik\u03b4jm + \u03b4im\u03b4jk)\u03b4ln +B6(\u03b4ik\u03b4jn + \u03b4in\u03b4jk)\u03b4lm +B7(\u03b4il\u03b4jm + \u03b4im\u03b4jl)\u03b4kn +B8(\u03b4il\u03b4jn + \u03b4in\u03b4jl)\u03b4km +B9(\u03b4im\u03b4jn + \u03b4in\u03b4jm)\u03b4kl; (5.12) with B1 = L1, B2 = L2, B3 = L3, B4 = L4 = L7, B5 = L5 = L10, B6 = L6 = L13, B7 = L8 = L11, B8 = L9 = L14, B9 = L12 = L15. (5.13)", "mime": "application/pdf"}, {"id": "ejde-489", "words": "4442", "extension": ".pdf", "flesch": "84", "author": "Zhan, Huashui; Feng, Zhaosheng", "title": "Stability of anisotropic parabolic equations without boundary conditions", "date": "2020", "keywords": "ai(x", "summary": "if x \u2208 \u2202\u2126, and ai(x) > 0 if x \u2208 \u2126, without any boundary conditions. When a(x) \u2208 C1(\u2126), and a(x) > 0, x \u2208 \u2126 and a(x)", "mime": "application/pdf"}, {"id": "ejde-49", "words": "41571", "extension": ".pdf", "flesch": "78", "author": "Hafstein, Sigurdur Freyr Hafstein", "title": "An algorithm for constructing Lyapunov functions", "date": "2007", "keywords": "autonomous; define; definition; equilibrium; function; j+1; linear; lyapunov; lyapunov function; mon; origin; p \u2208; problem; programming; set; solution; system; theorem; y \u2208; y(z; \u03c3 \u2208; \u2208 sp; \u2208 u", "summary": "\u2208 J for all x \u2208 I \\ C. It is clear from elementary calculus, that if g : I \u2192 R is a function from a nonempty open subset I \u2282 R into R and y \u2208 I, then all four Dini derivatives D+g(y), D+g(y), D\u2212g(y), and D\u2212g(y) of g at the point y exist.", "mime": "application/pdf"}, {"id": "ejde-490", "words": "4674", "extension": ".pdf", "flesch": "84", "author": "Tuan Duy, Nguyen; Nguyen, Huy Bac", "title": "Cylindrical Hardy inequalities on half-spaces", "date": "2020", "keywords": "hardy; inequalities; |y|", "summary": "[26] Goldstein, J. A.; Kombe, I.; Yener, A.; A unified approach to weighted Hardy type inequalities on Carnot groups. [4] Barbatis, G.; Filippas, S.; Tertikas, A.; A unified approach to improved Lp Hardy inequalities with best constants.", "mime": "application/pdf"}, {"id": "ejde-491", "words": "10620", "extension": ".pdf", "flesch": "73", "author": "Schulz-Baldes, Hermann; Urban, Liam", "title": "Space versus energy oscillations of Prufer phases for matrix Sturm-Liouville and Jacobi operators", "date": "2020", "keywords": "eigenvalues; energy; jacobi; liouville; matrix; phases; pru\u0308fer; sin; sturm", "summary": "Let us note that SE1 = E \u2212 V1 , SE2 = (E \u2212 V1)T\u22121 2 (E \u2212 V2)T\u22121 2 (E \u2212 V1)\u2212 (E \u2212 V1) , and that there is a recurrence relation SEn = (\u03c6En ) Even though the particular form of matrix Sturm-Liouville operator may not be of great importance, let us spell it out explicitly anyhow.", "mime": "application/pdf"}, {"id": "ejde-493", "words": "12100", "extension": ".pdf", "flesch": "91", "author": "Naumkin, Pavel I.; Sanchez-Suarez, Isahi", "title": "KdV type asymptotics for solutions to higher-order nonlinear Schrodinger equations", "date": "2020", "keywords": "ejde-2020/77; equation; estimate; lemma; naumkin; nonlinear; operator; order; proof; schro\u0308dinger; \u00b5(xt\u22122/3; \u03c6(0", "summary": "Let the weights P \u2208 C1(R \\ 0) and Q \u2208 C2(R \\ 0) be such that \u2202k\u03b7P (\u03b7) = O(|\u03b7|\u03b11\u2212k), k = 0, 1, and \u2202k\u03beQ(\u03be) = O(|\u03be|\u03b12\u2212k), k = 0, 1, 2. Suppose that 8 P. I. NAUMKIN, I. SA\u0301NCHEZ-SUA\u0301REZ EJDE-2020/77 h(\u03be) \u2208 C4(R \\ 0) is such that |\u2202k\u03be h(\u03be)| \u2264 C|\u03be|\u03b13\u2212k for \u03be \u2208 R \\ 0, 0 \u2264 k \u2264 4. |\u03be\u0302|6\u3008\u03be\u0302\u3009\u22126 i\u03be \u039b\u2032\u2032(\u03be) |\u03d5\u0302|2\u03d5\u0302+O(|\u03be\u0302|\u3008\u03be\u0302\u3009\u2212\u22121\u2212\u03bd\u2016\u03d5\u0302\u20163Y ) holds for all t \u2265 1 and \u03be \u2208 R, where \u03d5\u0302(t) = FU(\u2212t)u(t), \u03bd > 0 is small.", "mime": "application/pdf"}, {"id": "ejde-494", "words": "7350", "extension": ".pdf", "flesch": "86", "author": "Wang, Wenbo; Li, Quanqing", "title": "Existence and concentration of positive ground states for Schrodinger-Poisson equations with competing potential functions", "date": "2020", "keywords": "lemma; lim; schro\u0308dinger", "summary": "1 2 W. WANG, Q. LI EJDE-2020/78 potential and double parameters perturbation: \u2212\u03b52\u2206u+ V (x)u+ \u03c6u = u5 + f(u), x \u2208 R3, \u2212\u03b52\u2206\u03c6 = u2, u(x) > 0, x \u2208 R3. They multiply the nonlinearity by a potential b(x), that is, \u2212\u03b52\u2206u+ V (x)u+ \u03c6u = u5 + b(x)f(u), x \u2208 R3, \u2212\u03b52\u2206\u03c6 = u2, u(x) > 0, x \u2208 R3.", "mime": "application/pdf"}, {"id": "ejde-496", "words": "4097", "extension": ".pdf", "flesch": "76", "author": "Wang, Shaoqing; Yang, Jiazhong", "title": "Period functions and critical periods of piecewise linear system", "date": "2020", "keywords": "linear; period; piecewise; system", "summary": "Some orbits of piecewise linear system X in Section 3 In more detail, the trajectories of X = (X1, X2) in Figure 5 show that A6B4, B3B4, B3A3, A4B2, B1B2 and B1A1 all consist of sliding or escaping points (see the dashed lines in Figure 6), consequently, the closed orbits can only intersect three lines: PA5A6, A3A4 and A1A2Q. , nm, there exist two types of piecewise linear systems: one has a period annulus possessing exactly n critical periods; the other has m period annuli possessing exactly n1, n2, . . .", "mime": "application/pdf"}, {"id": "ejde-499", "words": "1594", "extension": ".pdf", "flesch": "72", "author": "D'Onofrio, Luigi", "title": "G-convergence of elliptic operators in non divergence form in R^n", "date": "2023", "keywords": "convergence; operators", "summary": "The aim of this note is to prove a characterization of the G-limit of a sequence of elliptic operators in non-divergence form. The Dirichlet problem (1.1) has unique solution in the plane, but differently from elliptic operator in divergence form, we need extra assumptions to guarantee the solvability of (1.1).", "mime": "application/pdf"}, {"id": "ejde-50", "words": "32542", "extension": ".pdf", "flesch": "81", "author": "Brooks, Robert M.; Schmitt, Klaus", "title": "The contraction mapping principle and some applications", "date": "2009", "keywords": "case; constant; contraction; contraction mapping; d(t; define; ejde-2009; following; function; mapping; mapping t; metric; mon; norm; point; principle; proof; sequence; set; solution; space; theorem; \u2208 e", "summary": "\u03b1i \u2264 \u03bei \u2264 \u03b2i, 1 \u2264 i \u2264 N}, (B = \u220fN i=1[\u03b1i, \u03b2i]), where the numbers \u03b1i, \u03b2i, 1 \u2264 i \u2264 N , are fixed real numbers (for each box). A positive mapping T is called homogeneous of degree p, p \u2265 0, whenever T (\u03bbu) = \u03bbpT (u), \u2200\u03bb > 0, u \u2208 K. A positive mapping is called monotone provided that u, v \u2208 K, u \u2264 v, imply T (u) \u2264 T (v).", "mime": "application/pdf"}, {"id": "ejde-500", "words": "9945", "extension": ".pdf", "flesch": "58", "author": "Pantha, Buddhi; Agusto, Folashade B.; Elmojtaba, Ibrahim M.", "title": "Optimal control applied to a visceral leishmaniasis model", "date": "2020", "keywords": "canine; control; disease; humans; leishmaniasis; model; number; parameters; population; rate; reservoir; sandflies; values", "summary": "Visceral leishmanisis; PKDL; vaccination; canine reservoir; optimal control. And we seek to find optimal controls, u\u22171, u \u2217 2 and u\u22173, such that J(u\u22171, u \u2217 2, u \u2217 3) = min (u1,u2,u3)\u2208U {J(u1, u2, u3)} (4.3) where the admissible set is U = {(u1, u2, u3) \u2208 (L\u221e(0, T ))3 : 0 \u2264 ui \u2264Mi;Mi \u2208 R+, i = 1, 2, 3}.", "mime": "application/pdf"}, {"id": "ejde-501", "words": "10929", "extension": ".pdf", "flesch": "74", "author": "Chhetri, Maya; Girg, Petr; Hollifield, Elliott", "title": "Existence of positive solutions for fractional Laplacian equations: theory and numerical experiments", "date": "2020", "keywords": "a.e; fractional; solutions; theorem", "summary": "We prove the existence of positive weak solution for classes of sublin- ear nonlinearities including logistic type. Next, using the method of sub- and supersolutions we establish the existence of positive weak solutions to (1.1) for classes of nonlinearities: sublinear at infinity, weighted logistic problems, and logistic problems with constant yield harvesting.", "mime": "application/pdf"}, {"id": "ejde-502", "words": "11740", "extension": ".pdf", "flesch": "68", "author": "Iagar, Razvan Gabriel; Munoz, Ana I.; Sanchez, Ariel", "title": "Qualitative properties of solutions to a reaction-diffusion equation with weighted strong reaction", "date": "2023", "keywords": "cauchy; problem; reaction; solutions", "summary": "It is also shown in [26] that such solution lies below any solution (and supersolution) to (1.5) and consequently also below any solution to (1.1) (which is a strict supersolution to (1.5)). To state our results concerning the qualitative theory of solutions to (1.1), we first have to introduce the notion of weak solution that will be used throughout the paper.", "mime": "application/pdf"}, {"id": "ejde-504", "words": "7972", "extension": ".pdf", "flesch": "75", "author": "de Lima, Henrique F.; Ramalho, Andre F. A.; Velasquez, Marco Antonio L.", "title": "Solutions to mean curvature equations in weighted standard static spacetimes", "date": "2020", "keywords": "curvature; function; spacelike", "summary": "= \u3008N,\u2207XY \u3009 = \u3008N,\u2207X\u2217Y \u3009 \u2212 \u3008X,Y \u3009 \u03c12 \u3008N,\u2207Y Y \u3009 = 1 \u03c1 \u3008X,\u2207\u03c1\u3009\u3008N,Y \u3009 \u2212 1 \u03c1 \u3008X,Y \u3009\u3008N,\u2207\u03c1\u3009. The metric induced on Pn from the Lorentzian metric (2.1) via \u03a3(z) is given by \u3008, \u3009z = \u3008, \u3009P \u2212 \u03c12dz2.", "mime": "application/pdf"}, {"id": "ejde-505", "words": "10305", "extension": ".pdf", "flesch": "82", "author": "Han, Bang-Sheng; Chang, Meng-Xue; Yang, Yinghui", "title": "Spatial dynamics of a nonlocal bistable reaction diffusion equation", "date": "2020", "keywords": "equation; solution; u(x", "summary": "satisfies \u2212 u\u2032\u2032 \u2212 cu\u2032 = ku(u\u2212 u0)(u\u2212 \u2212 u) + \u03c4ku2(u\u2212 \u03c6 \u2217 u) \u2264 ku2 \u2264 kMu. Then \u2223\u2223\u2223\u2223\u2223\u2223 b\u2212 dl2 \u2212 \u03bb \u2212 1 2 (k \u2212 2b+ \u221a k2 \u2212 4kb) \u2212 1 2 (k \u2212 2b+ \u221a k2 \u2212 4kb) 3a2 \u03c32 \u2212 a2 \u03c32 \u2212 l2 0", "mime": "application/pdf"}, {"id": "ejde-506", "words": "5053", "extension": ".pdf", "flesch": "83", "author": "Jin, Kun-Peng; Liang, Jin; Xiao, Ti-Jun", "title": "Stability of initial-boundary value problem for quasilinear viscoelastic equations", "date": "2020", "keywords": "\u222b t; \u222b \u03c9", "summary": "Clearly, we can rewrite the first equation in (1.1) as |ut|\u03c1utt \u2212\u2206utt \u2212 ( 1\u2212 \u222b t 0 g(s)ds ) \u2206u\u2212 \u222b t 0 g(t\u2212 s) (\u2206u(t)\u2212\u2206u(s)) = ( 1\u2212 \u222b t 0 g(s)ds )\u222b \u2126 u\u2206udx+ \u222b \u2126 u(t) \u222b t 0 g(t\u2212 s) (\u2206u(t)\u2212\u2206u(s)) ds dx + \u222b \u2126 |\u2207ut|2dx+ 1 \u03c1+ 1 \u222b \u2126 |ut|\u03c1+2dx = \u2212 ( 1\u2212 \u222b t 0 g(s)ds )\u222b \u2126 |\u2207u|2dx \u2212 \u222b \u2126 \u2207u(t) \u00b7 \u222b t 0 g(t\u2212 s) (\u2207u(t)\u2212\u2207u(s))", "mime": "application/pdf"}, {"id": "ejde-507", "words": "7441", "extension": ".pdf", "flesch": "78", "author": "Zhu, Jiazhen; Zhou, Jiazheng; Lin, Zhigui", "title": "Dynamics of a diffusive competitive model on a periodically evolving domain", "date": "2020", "keywords": "problem; solution; \u03c9(0", "summary": "Denote V 43 = M \u2212 V 42 . Noticing that V3 = M \u2212 V2, we have V 3 = M \u2212 V 2 = M = M \u2212 V 1 = V 3.", "mime": "application/pdf"}, {"id": "ejde-508", "words": "6108", "extension": ".pdf", "flesch": "79", "author": "Bhuyan, Ajit Kumar; Padhy, Laxmi Narayan; Rath, Radhanath", "title": "Oscillatory behavior for nonlinear homogeneous neutral difference equations of second order with coefficient changing sign", "date": "2020", "keywords": "proof; solution", "summary": "As of now, many researchers all over the world are engaged to find necessary or sufficient conditions for oscillation or non oscillation for neutral difference equations, because of its important applications in different fields of science and technology. Application to neutral difference equations with oscillating coefficients", "mime": "application/pdf"}, {"id": "ejde-510", "words": "7360", "extension": ".pdf", "flesch": "80", "author": "Bouhoufani, Oulia; Messaoudi, Salim A.; Zahri, Mostafa", "title": "Existence and decay of solutions to coupled systems of nonlinear wave equations with variable exponents", "date": "2023", "keywords": "t s", "summary": "A pair of functions (u, v) is said to be a weak solution of (1.1) on [0, T ), if u, v \u2208 L\u221e((0, T ), H1 0 (\u2126)), ut, vt \u2208 L\u221e((0, T ), L2(\u2126)), ut \u2208 Lm(\u00b7) \u03b1 (\u2126\u00d7 (0, T )), vt \u2208 Lr(\u00b7)\u03b2 (\u2126\u00d7 (0, T )) and (u, v) satisfies\u222b \u2126 ut\u03c6dx\u2212 \u222b \u2126 u1\u03c6dx+ \u222b t 0 \u222b \u2126 \u03b1(\u03c4)|ut|m(x)\u22122ut\u03c6dx d\u03c4 + \u222b t 0 \u222b \u2126 \u2207u.\u2207\u03c6dx d\u03c4 + \u222b t 0 \u222b \u2126 |u|p(x)\u22122u|v|p(x)\u03c6dx d\u03c4 = 0 and \u222b \u2126 vt\u03c8 dx\u2212 \u222b \u2126 v1\u03c8 dx+ \u222b t 0 \u222b \u2126 \u03b2(\u03c4)|vt|r(x)\u22122vt\u03c8 dx d\u03c4 + \u222b t 0 \u222b \u2126 \u2207v.\u2207\u03c8 dx d\u03c4 + \u222b t 0 \u222b \u2126 |v|p(x)\u22122v|u|p(x)\u03c8 dx d\u03c4 = 0, for all \u03c6, \u03c8 \u2208 H1 0 (\u2126) and all t \u2208 (0, T ), with (u(\u00b7, 0), v(\u00b7, 0)) = {w : \u2126\u00d7 (0, T )\u2192 R : \u222b T 0 \u222b \u2126 \u03b2(\u03c4)|w(x, \u03c4)|r(x) dx d\u03c4 < +\u221e}.", "mime": "application/pdf"}, {"id": "ejde-511", "words": "7724", "extension": ".pdf", "flesch": "81", "author": "Bao, Xiongxiong; Li, Ting", "title": "Existence and stability of traveling waves for a competitive-cooperative recursion system", "date": "2020", "keywords": "1+r1; system; wave", "summary": "If a2\u2212b1 a1a2\u2212b1c2 > 0, a1\u2212c2 a1a2\u2212b1c2 > 0 and a1a2 66= b1c2, then there is a nonnegative equilibrium (u\u0306+, v\u0306+, 0) = ( a2 \u2212 b1 a1a2 \u2212 b1c2 , a1 \u2212 c2 a1a2 \u2212 b1c2 , 0 ) . = (\u03a61(x \u2212 cn),\u03a62(x \u2212 cn),\u03a63(x \u2212 cn)) with speed c satisfies \u03a6(\u2212\u221e)", "mime": "application/pdf"}, {"id": "ejde-512", "words": "6276", "extension": ".pdf", "flesch": "83", "author": "Boutaous, Fatiha", "title": "Fractional-power approach for the study of elliptic second-order boundary-value problems with variable-operator coefficients in an unbounded domain", "date": "2020", "keywords": "+ \u221e; k\u03bb(x)\u2212; \u222b +", "summary": "= \u2212 1 2\u03c0i \u222b \u0393 e\u2212 \u221a \u2212zx(K \u2212 zI)\u22121\u03d5dz + 1 4\u03c0i \u222b \u0393 \u222b x 0 e\u2212 \u221a \u2212z(x\u2212s) \u221a \u2212z (1\u2212 e\u22122 \u221a \u2212zs)(K \u2212 zI)\u22121f(s) ds dz + 1 4\u03c0i \u222b \u0393 \u222b +\u221e x e\u2212 \u221a \u2212z(s\u2212x) \u221a \u2212z (1\u2212 e\u22122 \u221a \u2212zx)(K \u2212 zI)\u22121f(s)dsdz = exK\u03d5\u2212 1 2 \u222b It follows that \u2016A\u03bb(x)m0(x, g\u2217)\u2016X \u2264 C \u222b \u0393 (\u222b +\u221e 0 e\u2212C0(x+s)|z|ds ) \u2016g\u2217\u2016C\u221e([0,\u221e);X)d|z| \u2264 C (\u222b \u0393 e\u2212C0x|z| |z| d|z| ) \u2016g\u2217\u2016C\u221e([0,\u221e);X) <", "mime": "application/pdf"}, {"id": "ejde-514", "words": "10077", "extension": ".pdf", "flesch": "81", "author": "Manna, Utpal; Ashirbad Panda, Akash", "title": "Local existence and blow-up criterion for the two and three dimensional ideal magnetic Benard problem", "date": "2020", "keywords": "\u03c3(rn; \u20162l2", "summary": "For R\u2032 > R, using the property of Fourier truncation operator provided 0 < \u03b5 < s\u2212 1, the first term of (3.19) becomes\u2223\u2223\u2223((SR \u2212 SR\u2032)[(uR \u00b7 \u2207)uR],uR \u2212 uR \u2032)\u2223\u2223\u2223 \u2264 \u2016(SR \u2212 SR\u2032)[(uR \u00b7 \u2207)uR]\u2016L2 \u03c3 \u2016uR \u2212 uR \u2032 \u2016L2 \u03c3 \u2264 C R\u03b5 \u2016(uR \u00b7 \u2207)uR\u2016H\u03b5\u03c3\u2016u R \u2212 uR \u2032 \u2016L2 \u03c3 = C R\u03b5 \u2016\u2207 \u00b7 (uR \u2297 uR)\u2016H\u03b5\u03c3\u2016u R \u2212 uR \u2032 \u2016L2 \u03c3 \u2264 C R\u03b5 \u2016uR \u2297 uR\u2016Hs\u03c3\u2016u R \u2212 uR \u2032 \u2016L2 \u03c3 \u2264 C R\u03b5 \u2016uR\u20162Hs\u03c3\u2016u R \u2212 uR \u2032 \u2016L2 \u03c3 . (3.20) \u2207)uR],uR \u2212 uR \u2032 ) + ( SR\u2032 [(uR \u2032 \u00b7 \u2207)(uR \u2212 uR \u2032 )],uR \u2212 uR \u2032 ) .", "mime": "application/pdf"}, {"id": "ejde-515", "words": "6784", "extension": ".pdf", "flesch": "71", "author": "da Silva, Severino Horacio", "title": "Asymptotic behavior for a non-autonomous model of neural fields with variable external stimuli", "date": "2020", "keywords": "function", "summary": "Let us fix \u03b5 > 0 and t \u2208 R. Thus choose \u03c4 \u2208 R, \u03c4 \u2264 t, such that distH(TS0 (t, \u03c4)B(0, R),AS0 (t)) Moreover if |f(t, x)\u2212 f(t, y)| \u2264 C2(t)(1 + |x|p\u22121 + |y|p\u22121)|x\u2212 y|, (2.9) for any (x, y) \u2208 RN\u00d7RN , t \u2208 R, and for some strictly positive function C2 : R\u2192 R, then, for any 1 \u2264 p <\u221e, the function F is locally Lipschitz continuous on bounded sets with respect to the second variable.", "mime": "application/pdf"}, {"id": "ejde-517", "words": "11701", "extension": ".pdf", "flesch": "82", "author": "Mendoza, Renier; Keeling, Stephen", "title": "Existence of solution for a segmentation approach to the impedance tomography problem", "date": "2020", "keywords": "h1(\u03c9; inequality; lemma; problem; \u03b4\u03c71; \u03b4\u03c7\u03b41; \u03c7\u03b41", "summary": "Suppose \u2126 \u2286 Rn is a bounded domain with a sufficiently smooth bound- ary. In the forward EIT problem, given the boundary currents f \u2208 L2(\u2202\u2126) and the conductivity distribution \u03c3 \u2208 L\u221e(\u2126) satisfying \u03c3(x) \u2265 \u03c3 > 0, for all x \u2208 \u2126, the electric potential \u03c6 in \u2126 and the boundary voltage V = \u03c6 \u2223\u2223 \u2202\u2126 are solved.", "mime": "application/pdf"}, {"id": "ejde-519", "words": "4888", "extension": ".pdf", "flesch": "75", "author": "Hao, Jianghao; Lv, Mengxian", "title": "Energy decay for variable coefficient viscoelastic wave equation with acoustic boundary conditions in domains with nonlocally reacting boundary", "date": "2020", "keywords": "boundary; decay; equation; wave", "summary": "In this article, we study a variable coefficients viscoelastic wave equation with acoustic boundary conditions in domains with nonlocally re- acting boundary. Variable coefficients; viscoelastic wave equation; acoustic boundary conditions; nonlocally reacting boundary.", "mime": "application/pdf"}, {"id": "ejde-52", "words": "6098", "extension": ".pdf", "flesch": "82", "author": "Belaidi, Benharrat; Biswas, Tanmay", "title": "Growth properties of solutions of complex differential equations with entire coefficients of finite (alpha,beta,gamma)-order", "date": "2023", "keywords": "\u03b2(log; \u03b3(r; \u03b3)[f; \u03c3(\u03b1(log),\u03b2", "summary": "[2] B. Bela\u0308\u0131di; Estimation of the hyper-order of entire solutions of complex linear ordinary dif- ferential equations whose coefficients are entire functions. Since \u03b3(r +R0) \u223c \u03b3(r) as r \u2192 +\u221e, it follows that \u03c3(\u03b1(log),\u03b2,\u03b3)[f \u2032] = lim sup r\u2192+\u221e \u03b1(log[3]M(r, f \u2032)) \u03b2(log \u03b3(r)) \u2264 lim sup r\u2192+\u221e (\u03b1(log[3]M(r + 1, f))", "mime": "application/pdf"}, {"id": "ejde-520", "words": "9497", "extension": ".pdf", "flesch": "86", "author": "Kurima, Shunsuke", "title": "Time discretization of an abstract problem from linearized equations of a coupled sound and heat flow", "date": "2020", "keywords": "lemma; m\u22121\u2211", "summary": "h2(\u03a6\u03bb\u03d5\u03bb, \u03d5\u03bb)H = (g, \u03d5\u03bb)H \u2212 h2(L\u03d5\u03bb \u2212 L0, \u03d5\u03bb)H \u2212 h2(L0, \u03d5\u03bb)H \u2212 \u03b7h2(B2(I + hA1)\u22121\u03d5\u03bb, \u03d5\u03bb)H \u2264 cL 2 \u2016\u03d5\u03bb\u20162H + 1 2cL \u2016g\u20162H + CLh 2\u2016\u03d5\u03bb\u20162H + \u2016L0\u20162H 2 h2 + 1 2 h2\u2016\u03d5\u03bb\u20162H + \u03b7CA1,B2 (h+ h2)\u2016\u03d5\u03bb\u20162H , whence the conditions (A2) and (A3), the monotonicity of B1 and \u03a6\u03bb imply that there exists h1 \u2208 (0,min{1, h\u0303}) such that for all h \u2208 (0, h1) there exists a constant C2 = C2(h) > 0 satisfying \u2016\u03d5\u03bb\u20162V \u2264 C2 (3.3) for all \u03bb > 0. (4.17) Condition (A6) and Lemma 4.1 mean that there exists a constant C1 = C1(T ) > 0 such that \u2212 h (\u03a6\u03d5n+1 \u2212 \u03a6\u03d5n h , zn+1 ) H \u2264 C\u03a6h(1 + \u2016\u03d5n+1\u2016pV + \u2016\u03d5n\u2016qV )\u2016vn+1\u2016V \u2016zn+1\u2016H \u2264 C1h\u2016vn+1\u2016V \u2016zn+1\u2016H (4.18) for all h \u2208 (0, h2).", "mime": "application/pdf"}, {"id": "ejde-521", "words": "13056", "extension": ".pdf", "flesch": "80", "author": "Barbosa, Pricila S.; Pereira, Antonio L.", "title": "Continuity of attractors for C^1 perturbations of a smooth domain", "date": "2020", "keywords": "attractors; bounded; lemma; problem; theorem; \u03b5 u; \u2217\u22121", "summary": "\u2212 w2\u2016X\u03b7\u2016\u03a6\u2016X1/2 , where K1 is the embedding constant of X1/2 into Lq(\u2126), K2 is the embedding constant of X\u03b7 in L\u221e(\u2126) and w1(x) \u2264 \u03bex \u2264 w2(x) or w2(x) \u2264 \u03bex \u2264 w1(x). \u2264 \u03bex \u2264 w2(x).", "mime": "application/pdf"}, {"id": "ejde-523", "words": "11101", "extension": ".pdf", "flesch": "87", "author": "Biswas, Reshmi; Tiwari, Sweta", "title": "Nehari manifold approach for fractional p(.)-Laplacian system involving concave-convex nonlinearities", "date": "2020", "keywords": "+ +; lemma; m\u2192\u221e; \u2212 \u222b", "summary": "(5.2) Set fm(x, t) := |um \u2212 tu|\u03b1(x)\u22122(um \u2212 tu)|vm|\u03b2(x) gm(x, t) := |um \u2212 u|\u03b1(x)|vm \u2212 tv|\u03b2(x)\u22122(vm \u2212 tv). \u2212 u|\u03b1(x)|vm \u2212 v|\u03b2(x)dx = lim m\u2192\u221e \u222b \u2126 |um|\u03b1(x)|vm|\u03b2(x)dx\u2212 \u222b \u2126 |u|\u03b1(x)|v|\u03b2(x)dx (5.1) 26 R. BISWAS, S. TIWARI EJDE-2020/98 For t \u2208 (0, 1), we note that\u222b \u2126 \u222b 1 0 \u03b1(x)|um \u2212 tu|\u03b1(x)\u22122(um \u2212 tu)u|vm|\u03b2(x) dx dt \u2212 \u222b \u2126 \u222b 1 0 \u03b2(x)|um", "mime": "application/pdf"}, {"id": "ejde-524", "words": "5343", "extension": ".pdf", "flesch": "82", "author": "Wei, Yuanhong; Tian, Jian", "title": "Asymptotically linear and superlinear elliptic equations with gradient terms", "date": "2020", "keywords": "lemma", "summary": "Introduction This article concerns the existence of solutions for nonlinear elliptic equations with a gradient term, \u2212\u2206u = f(x, u,\u2207u) in \u2126, u = 0 on \u2202\u2126, (1.1) where \u2126 \u2282 Rn, n \u2265 1, is bounded, smooth and open with the boundary \u2202\u2126, f : The existence of solution was established while f satisfies the classical condition by Ambrosetti-Rabinowitz [2]: (AR) there exist \u03bd > 2 and t0 > 0 such that 0 < \u03bdF (x, s, \u03be) \u2264 sf(x, s, \u03be), x \u2208 \u2126, t \u2265 t0, \u03be \u2208 Rn, where F (x, s, \u03be) = \u222b", "mime": "application/pdf"}, {"id": "ejde-526", "words": "5382", "extension": ".pdf", "flesch": "87", "author": "Benali, Aharrouch; Jaouad, Bennouna", "title": "Nonlinear degenerate elliptic equations in weighted Sobolev spaces", "date": "2020", "keywords": "function", "summary": "\u2212 Tk(u)| \u2264 \u03b7}; and since {x \u2208 \u2126 : |u\u03b5 \u03b1 0 \u03c6(0, s)\u2212 \u03c6(k, s)ds = 1 \u03b1 \u222b |u|<k \u03bd(x)|\u2207u|p dx \u2264 ck \u03bb \u03b1 , which by (3.1) gives \u03c6(0, \u03b1) \u2264 c1k\u2212p1 + c2 k\u03bb \u03b1 .", "mime": "application/pdf"}, {"id": "ejde-53", "words": "6356", "extension": ".pdf", "flesch": "85", "author": "Huang, Lanxin; Su, Jiabao", "title": "Multiple solutions for nonhomogeneous Schrodinger-Poisson system with p-Laplacian", "date": "2023", "keywords": "1,p", "summary": "EJDE-2023/28 SCHRO\u0308DINGER-POISSON SYSTEMS WITH p-LAPLACIAN 7\u222b R3 |un \u2212 u|p dx \u2264 C (\u222b R3 (|un|p\u22122un \u2212 |u|p\u22122u)(un \u2212 u) dx )p/2 . (3.4) It follows from (3.3) and (3.4) that\u222b R3 en + (|un|p\u22122un \u2212 |u|p\u22122u)(un \u2212 u) dx = o(1).", "mime": "application/pdf"}, {"id": "ejde-530", "words": "8910", "extension": ".pdf", "flesch": "93", "author": "Phuong, Le Thi; Thanh Long, Nguyen", "title": "Exponential decay and blow-up for nonlinear heat equations with viscoelastic terms and Robin-Dirichlet conditions", "date": "2020", "keywords": "i=1; n\u2211 i=1", "summary": ". , uN ) + Fi(x, t), (1.1) where 0 < x < 1, t > 0, 1 \u2264 i \u2264 N , with N \u2208 N and N \u2265 2, associated with boundary conditions \u2202u1 \u2202x (0, t)\u2212 h0u1(0, t) \u2202ui \u2202x ) + \u222b t 0 gi(t\u2212 s) \u2202 \u2202x ( \u00b5\u0304i(x, s) \u2202ui \u2202x (x, s) )", "mime": "application/pdf"}, {"id": "ejde-531", "words": "6373", "extension": ".pdf", "flesch": "85", "author": "Dore, Giovanni", "title": "Dirichlet problem for second-order abstract differential equations", "date": "2020", "keywords": "problem", "summary": "= c1 sin (( 2`n + 1 2 ) (\u03c0 \u2212 t) ) + c2 sin (( 2`n + 1 2 ) t ) . bn \u2212 bn+1 + \u221e\u2211 n=n+1 (bn+1 \u2212 bn) = bn \u2212 b1 + bn \u2212 bn+1 + lim n\u2192\u221e bn \u2212 bn+1 \u2264 2bn \u2212 2bn+1 \u2264 4 k \u2212 (1/4) .", "mime": "application/pdf"}, {"id": "ejde-532", "words": "7953", "extension": ".pdf", "flesch": "87", "author": "Deng, Jin; Xia, \u00a0Aliang; Yang, Jianfu", "title": "Positive vortex solutions and phase separation for coupled Schrodinger system with singular potential", "date": "2020", "keywords": "|x|2", "summary": "= E\u03b2n(un, vn) \u2264 I\u221e for all n \u2208 N. So, after passing to a subsequence, there exist u\u221e, v\u221e \u2208 H such that (un, vn) \u21c0 (u\u221e, v\u221e) weakly in H, (un, vn)\u2192 (u\u221e, v\u221e) strongly in L4(R2)\u00d7 L4(R2), (un, vn)\u2192 (u\u221e, v\u221e) a.e. in R2 \u00d7 R2. \u2207v \u2212 v\u2206\u03b8 = 0, x \u2208 RN , u, v \u2265 0, x \u2208 RN . (1.4) If we assume u(x) = u(|x|) and choose the angular coordinate in R2 as phase function, see [3, 4], that is, \u03b8(x) := \uf8f1\uf8f4\uf8f4\uf8f4\uf8f2\uf8f4\uf8f4\uf8f4\uf8f3 arctan x2 x1 , if x1 > 0, \u03c0 + arctan x2 x1 , if x1 < 0, \u03c0/2, if x1 = 0 and x2 > 0, \u2212\u03c0/2, if x1 = 0 and x2 < 0, (1.5) we obtain \u2206\u03b8 = 0, \u2207\u03b8 \u00b7 \u2207u = 0, |\u2207\u03b8|2 = 1 |x|2 , EJDE-2020/108 SCHRO\u0308DINGER SYSTEM WITH SINGULAR POTENTIAL 3 and the system reduces to \u2212\u2206u+ \u03bb1u+ k2 0 u |x|2 = \u00b51u 3 + \u03b2uv2, x \u2208 R2, \u2212\u2206v + \u03bb2v + k2 0 v |x|2 = \u00b52v 3 + \u03b2u2v, x \u2208 R2, u, v \u2265 0, x \u2208 R2.", "mime": "application/pdf"}, {"id": "ejde-534", "words": "11024", "extension": ".pdf", "flesch": "87", "author": "Ahmad, Bashir; Alsaedi, Ahmed; Berbiche, Mohamed; Kirane, Mokhtar", "title": "Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations", "date": "2020", "keywords": "solutions; time", "summary": "= N 2 \u03b31( 1 r1 \u2212 1 s1 ), \u03c31 + \u03b31 \u2212 N 2 \u03b31 ( p s2 \u2212 1 s1 ) \u2212 p\u03c32 = 0, \u03c31 + \u03b31 \u2212 N 2 \u03b31 ( p s2 \u2212 1 s1 ) + ( \u03b32 \u2212 N 2 \u03b32 ( q s1 \u2212 1 s2 ) \u2212 q\u03c31 ) p = 0, \u03c31 + \u03b31 \u2212 \u03b31\u03b4 + (\u03b32 \u2212 \u03b32\u03b4 \u2212 q\u03c31)p = 0. pq pq \u2212 1 + 4 \u03b31 (\u03b31 \u2212 1), (\u22124 1 q + ( 4 \u03b31 + 2N) 1 p\u2032q \u2212 4 + ( 4 \u03b31 + 2N) 1 q\u2032 ) pq pq \u2212 1 + 4 \u03b31 (\u03b31 \u2212 1) } , and \u03b42 = max { (\u2212 4 \u03b31 \u03b32 + ( 4 \u03b31 + 2N) 1 p\u2032 \u2212 4 1 p + ( 4 \u03b31 + 2N) 1 pq\u2032 ) pq pq \u2212 1 + 4 \u03b31 (\u03b32 \u2212 1), (\u22124 + ( 4 \u03b31 + 2N) 1 p\u2032 \u2212 4 1 p + ( 4 \u03b31 + 2N) 1 pq\u2032 ) pq pq \u2212 1 + 4 \u03b31 (\u03b32 \u2212 1) } .", "mime": "application/pdf"}, {"id": "ejde-535", "words": "5278", "extension": ".pdf", "flesch": "84", "author": "Dahan Kassim, Mohammed; Eddine Tatar, Nasser", "title": "Convergence of solutions of fractional differential equations to power-type functions", "date": "2020", "keywords": "fractional", "summary": "Asymptotic behavior; boundedness; fractional differential equation; Caputo fractional derivative; Riemann-Liouville fractional derivative. [21] M. Medved\u030c; Asymptotic integration of some classes of fractional differential equations, Tatra Mt. Math.", "mime": "application/pdf"}, {"id": "ejde-536", "words": "11238", "extension": ".pdf", "flesch": "89", "author": "Ma, Luyi; Niu, Hong-Tao; Wang, Zhi-Cheng", "title": "Pyramidal traveling fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R^3", "date": "2020", "keywords": "fronts; i=1,2; j=1; lemma; lim; pyramidal; sup; vi(x; v\u22122; x))\u03b2i", "summary": "= (u1(1 \u2212 r \u2212 u1 + ru2), bu1(1 \u2212 u2)). v\u22122 (x) = U2 ( c s (x3 \u2212 y3 + h(x\u2032 \u2212 y\u2032)) )", "mime": "application/pdf"}, {"id": "ejde-537", "words": "3762", "extension": ".pdf", "flesch": "75", "author": "Qiu, Haijing; Wang, Yan", "title": "Continuous dependence of recurrent solutions for stochastic differential equations", "date": "2020", "keywords": "equations; solutions; sup", "summary": "[6] and Ji et al [12] for periodic solutions for SDEs, see Halanay [10], Da Prato and Tudor [6] F. Chen, Y. Han, Y. Li, X. Yang; Periodic solutions of Fokker-Planck equations, J. Differen- tial Equations, 263 (2017), 285\u2013298.", "mime": "application/pdf"}, {"id": "ejde-539", "words": "6717", "extension": ".pdf", "flesch": "87", "author": "Pardo, Rosa; Sanjuan, Arturo", "title": "Asymptotic behavior of positive radial solutions to elliptic equations approaching critical growth", "date": "2020", "keywords": "lemma; lim; log(e+; n\u22122", "summary": "(i) From (2.5), Lemma 2.1, and (4.1) with t = T and r = 2\u2217 \u2212 1, we have y\u2032\u03b1(T ) [ln(e+ u)]\u03b1 , p\u2217 = Np N \u2212 p , \u03b1 > p (N \u2212 p) ; see [7].", "mime": "application/pdf"}, {"id": "ejde-540", "words": "4836", "extension": ".pdf", "flesch": "75", "author": "Heidarkhani, Shapour; Gharehgazlouei, Fariba; Imbesi, Maurizio", "title": "Existence and multiplicity of homoclinic solutions for a difference equation", "date": "2020", "keywords": "solutions; theorem", "summary": "= 1 p \u2016u\u2016p \u2212 \u2211 k\u2208Z H(u(k)) \u2200u \u2208 X, (2.2) \u03a8(u) := \u2211 k\u2208Z F (k, u(k)) \u2200 u \u2208 lp (2.3) where F (k, t) = \u222b t 0 f(k, \u03be)d\u03be for t \u2208 R and k \u2208 Z, H(t) = \u222b t 0 h(\u03be)d\u03be for t \u2208 R. Let I\u03bb : X \u2192 R be the energy functional associated to the problem (1.1) defined by I\u03bb(u) = \u03bbf(k, u(k)) + sin4( u(k) 2 ) \u2200k \u2208 Z, u(k)\u2192 0 as |k| \u2192 \u221e. For all (k, t) \u2208 Z\u00d7 R put f(k, t)", "mime": "application/pdf"}, {"id": "ejde-541", "words": "9706", "extension": ".pdf", "flesch": "79", "author": "Adhikari, Dhruba R.; Stachura, Eric", "title": "General p-curl systems and duality mappings on Sobolev spaces for Maxwell equations", "date": "2020", "keywords": "1,p; curl; domain; theorem", "summary": "(2.7) Thus, we see that W 0 N = W 1,p 0 (curl,\u2126) \u2229W Thus, we conclude that u \u2208 W 1,p 0 (curl,\u2126) (note that u\u0303(k) \u2208 (C\u221e0 (\u2126)) 3 for each k).", "mime": "application/pdf"}, {"id": "ejde-543", "words": "7331", "extension": ".pdf", "flesch": "86", "author": "Ding, Yuanlin; Feckan, Michal; Wang, Jinrong", "title": "Stability for conformable impulsive differential equations", "date": "2020", "keywords": "a)\u03b2; tn(a", "summary": "= g(t, y(t)), t \u2208 I := [a, b]\\{t1, . . . ,m, y(t) = \u03bey(t\u2212k ), t \u2208 (tk, sk], k = 1, 2, . . .", "mime": "application/pdf"}, {"id": "ejde-544", "words": "8015", "extension": ".pdf", "flesch": "91", "author": "Yang, Lu; Liu, Xiangqing; Zhou, Jianwen", "title": "Concentration of nodal solutions for semiclassical quadratic Choquard equations", "date": "2023", "keywords": "lemma; \u222b r3", "summary": "j,\u03b5,p|1 \u2264 j \u2264 k} such that \u0393(\u03bb) \u03b5,p (u (\u03bb) j,\u03b5,p) = cj(\u03b5, p, \u03bb) \u2264 c\u0303k, By Corollary 4.3, we have p\u2212 1 2 \u222b R3 ( 1 | \u00b7 | \u2217 (|un,p|p))|un,p|p\u22122\u03d52 dx \u2264 m\u2211 i=1 c \u222b R3 ( 1 | \u00b7 | \u2217 e\u2212c|x\u2212yn,i|)\u03d52 dx and p 2 \u222b R3 ( 1 | \u00b7 | \u2217 (|un,p|p\u22122un,p\u03d5))|un,p|p\u22122un,p\u03d5dx \u2264 m\u2211 i=1 c \u222b R3 ( 1 | \u00b7 | \u2217 (e\u2212c|x\u2212yn,i|\u03d5) ) e\u2212c|x\u2212yn,i|\u03d5dx + m\u2211 i 6=j c \u222b R3 ( 1 | \u00b7 | \u2217 (e\u2212c|x\u2212yn,j |\u03d5) ) e\u2212c|x\u2212yn,i|\u03d5dx \u2264 m\u2211 i=1 c \u222b R3 ( 1 | \u00b7 | \u2217 (e\u2212c|x\u2212yn,i|\u03d5) ) e\u2212c|x\u2212yn,i|\u03d5dx+ o(1)", "mime": "application/pdf"}, {"id": "ejde-545", "words": "11556", "extension": ".pdf", "flesch": "86", "author": "Rani, Anu; Goyal, Sarika", "title": "Polyharmonic systems involving critical nonlinearities with sign-changing weight functions", "date": "2020", "keywords": "2\u2212r; \u03bb,\u00b5; \u2212 r", "summary": "= (2\u2212 \u03b2 \u2212 \u03b3)t1\u2212\u03b2\u2212\u03b3\u2016(u, v)\u20162 \u2212 (r \u2212 \u03b2 \u2212 \u03b3)tr\u2212\u03b2\u2212\u03b3\u22121Q\u03bb,\u00b5(u, v), we obtain \u03be \u2032 (u,v)(t) Moreover, \u03be(u,v)(tmax) = ( (2\u2212 r)\u2016(u, v)\u20162 (\u03b2 + \u03b3 \u2212 r) \u222b \u2126 h(x)|u|\u03b2 |v|\u03b3dx ) 2\u2212r \u03b2+\u03b3\u22122 \u2016(u, v)\u20162 \u2212 ( (2\u2212 r)\u2016(u, v)\u20162 (\u03b2 + \u03b3 \u2212 r) \u222b \u2126 h(x)|u|\u03b2 |v|\u03b3dx ) \u03b2+\u03b3\u2212r \u03b2+\u03b3\u22122 \u222b \u2126 h(x)|u|\u03b2 |v|\u03b3dx = \u2016(u, v)\u2016r( 2\u2212 r \u03b2 + \u03b3 \u2212 r ) 2\u2212r \u03b2+\u03b3\u22122 (\u03b2 + \u03b3 \u2212 2 \u03b2 + \u03b3 \u2212 r )( \u2016(u, v)\u2016\u03b2+\u03b3\u222b \u2126 h(x)|u|\u03b2 |v|\u03b3dx ) 2\u2212r \u03b2+\u03b3\u22122 \u2265 \u2016(u, v)\u2016r( 2\u2212 r \u03b2 + \u03b3 \u2212 r ) 2\u2212r \u03b2+\u03b3\u22122 (\u03b2 + \u03b3 \u2212 2 \u03b2 + \u03b3 \u2212 r )(S \u03b2+\u03b3 2 |h|\u221e ) 2\u2212r \u03b2+\u03b3\u22122 .", "mime": "application/pdf"}, {"id": "ejde-546", "words": "3933", "extension": ".pdf", "flesch": "79", "author": "Devi, Darshana; Chutia, Duranta; Haloi, Rajib", "title": "Rothe's method for solving semi-linear differential equations with deviating arguments", "date": "2020", "keywords": "method", "summary": "= 1 \u0393(\u03b1) \u222b t 0 u(s) (t\u2212 s)1\u2212\u03b1 ds+ f(t), t \u2208 (0, T ], u(0) = u0, where 0 < \u03b1 < 1, -A is the infinitesimal generator of a C0-semigroup of contractions, f is a given map from [0, T ] to X, and the initial point u0 \u2208 D(A) \u2282 X, the domain of A. Dubey = f(t, u(t), ut), t \u2208 (0, T ], h(u0) = \u03c6 on [\u2212\u03c4, 0], where 0 < T < \u221e, \u03c6 \u2208 C0 := C([\u2212\u03c4, 0];X), \u03c4 > 0, the nonlinear operator A is single-valued and m-accretive defined from the domain D(A) \u2282 X to X, the nonlinear map f is defined from [0, T ]\u00d7X\u00d7C0 to X, the map h is defined from C0 to C0.", "mime": "application/pdf"}, {"id": "ejde-547", "words": "6167", "extension": ".pdf", "flesch": "79", "author": "Mansouri, Sabeur; Tebou, Louis", "title": "Stabilization of coupled thermoelastic Kirchhoff plate and wave equations", "date": "2020", "keywords": "equations; plate; system; thermoelastic; \u2016z\u20161/2\u03b3", "summary": "Consider the coupled thermoelastic Kirchhoff plate/wave system ytt \u2212 \u03b3\u2206ytt + a\u22062y + \u03b1\u2206\u03b8 + \u00b5z = 0 in \u2126\u00d7 (0,+\u221e), \u03b8t \u2212 \u03c3\u2206\u03b8 \u2212 \u03b2\u2206yt = 0 in \u2126\u00d7 (0,+\u221e), ztt \u2212 \u03b7\u2206z + \u00b5y = 0 in \u2126\u00d7 (0,+\u221e), y = \u2202\u03bdy = 0, \u03b8 = z = 0, on \u0393\u00d7 (0,+\u221e), y(x, 0) = y0, yt(x, 0) = y1, \u03b8(x, 0) = \u03b80 in \u2126, z(x, 0) = z0, zt(x, 0) = z1 in \u2126, (1.1) where a, \u03b7, \u03b3, \u03c3 are positive physical constants representing respectively, the flexural stiffness of the plate, wave speed, rotational force constant, and thermal conductiv- ity, while \u00b5 denotes the coupling parameter, and is a nonzero real number. We introduce the Hilbert space over the field C of complex numbers H\u03b3 := H2 0 (\u2126)\u00d7H1 0 (\u2126)\u00d7 L2(\u2126)\u00d7H1 0 (\u2126)\u00d7 L2(\u2126), EJDE-2020/121 THERMOELASTIC KIRCHHOFF PLATE AND WAVE EQUATIONS 3 equipped with the norm \u2016U\u20162H\u03b3 := a\u2016\u2206u\u20162 + \u03b3\u2016\u2207v\u20162 + \u2016v\u20162 + \u03b1 \u03b2 \u2016\u03b8\u20162 + \u03b7\u2016\u2207y\u20162 + \u2016z\u20162 + 2\u00b5 \u222b \u2126 Re(uy)d\u2126, (1.3) for all U = (u, v, \u03b8, y, z) \u2208 H\u03b3 .", "mime": "application/pdf"}, {"id": "ejde-548", "words": "5571", "extension": ".pdf", "flesch": "84", "author": "Yan, Jianlu; Li, Yuxiang", "title": "Existence and boundedness of solutions for a Keller-Segel system with gradient dependent chemotactic sensitivity", "date": "2020", "keywords": "\u222b \u03c9", "summary": "Finally, for arbitrary non-negative \u03c8 \u2208 C\u221e0 (\u2126\u0304\u00d7 [0,\u221e)), multiplying the second equation in (2.7) by \u03c8, and integrating by parts, we have\u222b \u2126 v0\u03c8(\u00b7, 0) + \u222b T 0 \u222b \u2126 v\u03b5\u03c8t = \u222b T 0 \u222b \u2126 \u2207v\u03b5 \u00b7 \u2207\u03c8 + \u222b T 0 \u222b \u2126 v\u03b5\u03c8 \u2212 \u222b T 0 \u222b \u2126 u\u03b5\u03c8 (3.19) for all \u03b5 \u2208 (0, 1). \u2212 \u03c7\u2207 \u00b7 ( u\u2207v\u221a 1 + |\u2207v|2 ) , 0 = \u2206v \u2212M + u, (1.5) where M = 1 |\u2126| \u222b \u2126 u0(x)dx, n \u2265 2 and \u03c7 < 1.", "mime": "application/pdf"}, {"id": "ejde-55", "words": "8914", "extension": ".pdf", "flesch": "85", "author": "Bu, Zhen-Hui; Wang, Chen-Lu; Zhang, Xin-Tian", "title": "Pyramidal traveling fronts of a time periodic diffusion equation with degenerate monostable nonlinearity", "date": "2023", "keywords": "fronts; i=1; periodic; \u03c8(x", "summary": "In addition, there exist positive constants L1, L2, L3, \u03b21 such that L1e \u039b2\u03be \u2264 \u03a8(\u03be, t), \u03a8\u03be(\u03be, t), |\u03a8\u03be\u03be(\u03be, t)| \u2264 L2e \u039b2\u03be, \u2200\u03be < 0, t \u2208 R, (1.4) |\u03a8(\u03be, t)\u2212 1|, \u03a8\u03be(\u03be, t), |\u03a8\u03be\u03be(\u03be, t)| \u2264 L3e \u2212\u03b21\u03be, \u2200\u03be > 0, t \u2208 R. (1.5) Since lim\u03d1\u2192\u2212\u221e\u03a8(\u03d1, t) = 0 uniformly for t \u2208", "mime": "application/pdf"}, {"id": "ejde-550", "words": "8836", "extension": ".pdf", "flesch": "91", "author": "Mahdi, Achache; Hossni, Tebbani", "title": "Maximal regularity for non-autonomous Cauchy problems in weighted spaces", "date": "2020", "keywords": "\u03b2(0; \u03c4 0", "summary": "(4.7) Integrating by parts, we obtain for t \u2208 [0, \u03c4 ] and f \u2208W 1,2 \u03b2,0(0, \u03c4,H) A(0)u(t) = A(0) \u222b t 0 e\u2212(t\u2212s)A(0)f(s) ds = f(t)\u2212 \u222b t 0 e\u2212(t\u2212s)A(0)f\u0307(s) ds = u\u0307(t) +A(0)u(t)\u2212 \u222b t 0 e\u2212(t\u2212s)A(0)f\u0307(s) ds. Let x \u2208 H and t \u2208", "mime": "application/pdf"}, {"id": "ejde-551", "words": "5414", "extension": ".pdf", "flesch": "83", "author": "Cabanillas Lapa, Eugenio", "title": "Global solutions for fractional viscoelastic equations with logarithmic nonlinearities", "date": "2020", "keywords": "log", "summary": "= 1 2 (g\u2032 \ufffd u)(t)\u2212 1 2 g(t)\u2016u(t)\u20162W0 \u2212 \u2016ut(t)\u201622 \u2212 a \u222b \u2126 |u(t)|r(x)\u22122u2 t (t) dx \u2212 \u03b5\u2016u(t)\u20162\u03b1W0 \u2212 \u03b5\u2016u(t)\u20162W0 + \u03b5 \u222b \u2126 uf(u) log |u(t)| dx + \u03b5 \u222b t 0 g(t\u2212 \u03c4)\u3008u(\u03c4), u(t)\u3009W0 d\u03c4. (3.36) + \u222b t 0 \u2016umt(t)\u201622 + a \u222b t 0 \u222b \u2126 |um(t)|r(x)\u22122|umt(t)|2 dx \u2264 Em(0).", "mime": "application/pdf"}, {"id": "ejde-552", "words": "12145", "extension": ".pdf", "flesch": "79", "author": "Bauer, Sean; Petrov, Nikola P.", "title": "Existence of KAM tori for presymplectic vector fields", "date": "2020", "keywords": "basis; form; invariant; kam; kj(\u03b8; lemma; matrix; section; td+n; vector", "summary": "= K\u2217\u03b8 \u03c9\u03b8, where K\u2217\u03b8 : T\u03b8Td+n \u2192 TK(\u03b8)P is the derivative of K at \u03b8 \u2208 Td+n and we consider \u03c9 \u2208 Rd+n as \u03c9\u03b8 \u2208 T\u03b8Td+n = Rd+n. \u2208 TK(\u03b8)K \u2286 TK(\u03b8)P is the value of V\u03bb\u0304 at K(\u03b8) \u2208 K, \u03c9\u03b8 \u2208 T\u03b8Td+n is the Diophantine vector \u03c9 considered as an element of T\u03b8Td+n = Rd+n, and K\u2217\u03b8 :", "mime": "application/pdf"}, {"id": "ejde-553", "words": "11001", "extension": ".pdf", "flesch": "83", "author": "da Silva Almeida Junior, Dilberto; Araujo Ramos, Anderson de Jesus; Pantoja Fortes, Joao Carlos; de Lima Santos, Mauro", "title": "Ingham type approach for uniform observability inequality of the semi-discrete coupled wave equations", "date": "2020", "keywords": "j=0 \u222b; observability; \u222b l; \u222b t", "summary": "= \u222b L 0 x\u03c6x\u03c6t dx and from where results that X\u03c6(t) \u2223\u2223T 0 + \u222b T 0 F (t)dt = \u03b1 \u222b T 0 \u222b = \u222b L 0 x\u03c8x\u03c8t dx and taking into account the energy defined by (2.45), we obtain X\u03c8(t) \u2223\u2223T 0 + \u222b T 0", "mime": "application/pdf"}, {"id": "ejde-555", "words": "8330", "extension": ".pdf", "flesch": "85", "author": "Li, Fengbai; Wang, Weike; Wang, Yutong", "title": "Pointwise estimates of solutions to conservation laws with nonlocal dissipation-type terms", "date": "2020", "keywords": "c(1; div; estimate; solution; wang", "summary": "For \u03a02,1, let \u2126 = [0, t]\u00d7 Rn, \u21261 = \u2126 \u2229 { t2 < \u03c4 \u2264 t}, \u21262 = \u2126 \u2229 {0 \u2264 \u03c4 \u2264 t 2}. Since 1 + |x|2 t \u2264 { 2, |x|2 \u2264 t, 2 |x| 2 t , |x| 2 \u2265 t, we have |D\u03b1 xG2(t, x)| \u2264 Ce\u2212 t 2m0BN (t, |x|), which completes the proof.", "mime": "application/pdf"}, {"id": "ejde-558", "words": "8546", "extension": ".pdf", "flesch": "88", "author": "Cely, Liliana", "title": "Stability of ground states of nonlinear Schrodinger systems", "date": "2023", "keywords": "j(\u03b7; lemma; log", "summary": "= 1 r\u2016\u2202x\u03c6\u2016L\u221e \u2264 C\u03b5; (ii) Since \u03c6r is identically 1 on |x \u2212 yn| \u2264 r and \u03c6r vanishes on |x \u2212 yn| \u2265 2r, then |\u03c6r|2 log |\u03c6r|2 vanishes on both |x \u2212 yn| \u2264 r and |x \u2212 yn| \u2265 2r. [0, \u03b7]\u00d7 [0, \u03b6] such that \u03b3 = \u03b7 + \u03b6 and J(\u00b51, \u00b52) + J(\u03b7 \u2212 \u00b51, \u03b6 \u2212 \u00b52) \u2264 J(\u03b7, \u03b6).", "mime": "application/pdf"}, {"id": "ejde-560", "words": "6239", "extension": ".pdf", "flesch": "82", "author": "Ahmad, Israr; Nieto, Juan Jose; Rahman, Ghaus ur; Shah, Kamal", "title": "Existence and stability for fractional order pantograph equations with nonlocal conditions", "date": "2020", "keywords": "differential; equations; fractional; |\u03bb1", "summary": "\u2212 \u03b41 \u2212 \u00b51)| , K2 |\u03bb2 \u2212 \u03b42 \u2212 \u00b52)| ) . \u2212 \u03b41 \u2212 \u00b51| \u2016x1 \u2212 x\u03041\u2016 , \u2016H2x2 \u2212H2x\u03042\u2016 \u2264 K2 |\u03bb2 \u2212 (\u03b42 + \u00b52)| \u2016x2 \u2212 x\u03042\u2016 .", "mime": "application/pdf"}, {"id": "ejde-561", "words": "10679", "extension": ".pdf", "flesch": "78", "author": "Zhang, Jiangwei; Xie, Zhe; Xie, Yongqin", "title": "Asymptotic behavior of solutions to nonclassical diffusion equations with degenerate memory and a time-dependent perturbed parameter", "date": "2024", "keywords": "attractors; equation; lemma; memory; process; time; u(t; xie; \u222b \u221e", "summary": "Assume that U(t, \u03c4) is a process on {Mt}t\u2208R and it has a pull- back bounded absorbing set B\u0303 = {Bt}t\u2208R. U(t, \u03c4) is called Mt-contractive process if for any given \u03b5 > 0, there exist T = T (\u03b5) and \u03c6t T (\u00b7, \u00b7) Hence, for each \u03b5 > 0, there exists \u03b4 = \u03b5 4 such that 2\u2225U(t, T )z1T \u2212 U(t, T )z2T \u22252Mt < \u03b5, (3.68) holds for any t \u2265 T = T (\u03b5) fixed.", "mime": "application/pdf"}, {"id": "ejde-562", "words": "6817", "extension": ".pdf", "flesch": "79", "author": "Perez-Lopez, Jhean E.; Rueda-Gomez, Diego A.; Villamizar-Roa, Elder J.", "title": "Existence of global solutions for cross-diffusion models in a fractional setting", "date": "2023", "keywords": "fractional; lemma", "summary": "For 1 \u2264 p < N \u2212 \u03bb, 1 \u03b1 < \u03ba and s\u2217 = N\u2212\u03bb p , we define the Banach spaces X1 and X2 by X1 = L\u0303\u221e([0,\u221e);N s\u2217\u2212\u03b8 p,\u03bb,\u221e) \u2229 L\u0303\u03ba([0,\u221e);N s\u2217\u2212\u03b8(1\u2212 1 \u03b1\u03ba ) p,\u03bb,\u221e ), X2 = L\u0303\u221e([0,\u221e);N s\u2217 p,\u03bb,\u221e), (2.8) 6 J. E. PE\u0301REZ-LO\u0301PEZ, D. A. RUEDA-GO\u0301MEZ, E. J. VILLAMIZAR-ROA EJDE-2023/77 endowed with the corresponding norms \u2016x\u2016X1 = \u2016x\u2016 L\u0303\u221e([0,\u221e);N s\u2217\u2212\u03b8p,\u03bb,\u221e) + \u2016x\u2016 L\u0303\u03ba([0,\u221e);N s\u2217\u2212\u03b8(1\u2212 1 \u03b1\u03ba ) p,\u03bb,\u221e ) , \u2016x\u2016X2 = \u2016x\u2016 L\u0303\u221e([0,\u221e);N s\u2217p,\u03bb,\u221e) . N \u2212 \u03bb, s\u2217 = N\u2212\u03bb p , and [n0,m0, v0] \u2208 N s\u2217\u2212\u03b8 p,\u03bb,\u221e \u00d7 N s\u2217\u2212\u03b8 p,\u03bb,\u221e \u00d7 N s\u2217 p,\u03bb,\u221e.", "mime": "application/pdf"}, {"id": "ejde-563", "words": "5554", "extension": ".pdf", "flesch": "84", "author": "Melo, Wilberclay G.; Rocha, Nata F.; Costa, Natielle dos Santos", "title": "Solutions for the Navier-Stokes equations with critical and subcritical fractional dissipation in Lei-Lin and Lei-Lin-Gevrey spaces", "date": "2023", "keywords": "equations; x sa", "summary": "Assume that f \u2208 X sa,\u03c3(R3). [\u22121, 0)\u00d7 (1,+\u221e) ) \u222a ( [0,+\u221e)\u00d7{0}\u00d7 [1,+\u221e) ) and u0 \u2208 X sa,\u03c3(R3).", "mime": "application/pdf"}, {"id": "ejde-564", "words": "6597", "extension": ".pdf", "flesch": "81", "author": "Wang, Lulu; Ma, Qiaozhen", "title": "Uniform attractors of non-autonomous suspension bridge equations with memory", "date": "2024", "keywords": "bridge; suspension", "summary": "= 0, y \u2208 (\u2212l, l), t \u2265 \u03c4, uyy(x,\u00b1l, t) + = 0, x \u2208 (0, \u03c0), t \u2265 \u03c4, (1.9) \u03b7t(0, y, s) = \u03b7txx(0, y, s) = \u03b7t(\u03c0, y, s) = \u03b7txx(\u03c0, y, s) = 0, y \u2208 (\u2212l, l), s \u2208 R+, \u03b7tyy(x,\u00b1l, s) +", "mime": "application/pdf"}, {"id": "ejde-568", "words": "5768", "extension": ".pdf", "flesch": "78", "author": "Song, Fei; Wang, Yuping; Akbarpoor, Shahrbanoo", "title": "Inverse nodal problems for Dirac operators and their numerical approximations", "date": "2023", "keywords": "inverse; nodal; solution", "summary": "Inverse nodal problems consist in recovering the potential Q(x) and the coefficients \u03b1, \u03b2 from the given subsets of the nodal points (zeros of eigenfunctions). This class of inverse nodal problems has been studied for the Sturm-Liouville operator", "mime": "application/pdf"}, {"id": "ejde-57", "words": "4082", "extension": ".pdf", "flesch": "74", "author": "Treinen, Raymond", "title": "Discussion of a uniqueness result in \"Equilibrium Configurations for a Floating Drop\"", "date": "2023", "keywords": "liquid; problem", "summary": "Then we use Chebyshev spectral methods to approximate solutions to certain boundary value problems used to check this hypothesis holds at least on a range of cases. Consider the intersection points of these curves with r = \u03c10.", "mime": "application/pdf"}, {"id": "ejde-571", "words": "5922", "extension": ".pdf", "flesch": "77", "author": "Chen, Wei", "title": "Variety of solutions and dynamical behavior for YTSF equations", "date": "2023", "keywords": "equation; lump; solution; wave; ytsf", "summary": "[22] Z. Y. Yan; New families of nontravelling wave solutions to a new (3+1)-dimensional potential- YTSF equation, Phys. In this section we will study the interaction between two-lump solution and soliton wave solution 4 W. CHEN EJDE-2023/82 (a) u0 = \u22122 (b) u0 = \u22121.5 (c) u0 = \u22121 (d) u0 = 0 (e) u0 = 1 (f) u0 = 1.5 (g) u0 = \u22122,\u22121.5,\u22121 (h) u0 = 0, 1, 1.5 (i) u0 = \u22121.5, 1.5 Figure 1.", "mime": "application/pdf"}, {"id": "ejde-572", "words": "23028", "extension": ".pdf", "flesch": "82", "author": "Jia, Man; Su, Youfeng; Chen, Hebai", "title": "Global analysis on a continuous planar piecewise linear differential system with three zones", "date": "2023", "keywords": "cycle; homoclinic; limit; linear; system; \u03c6(\u03b1; \u2208 r2", "summary": "= {(\u03b1, tc) \u2208 R2 : \u03b1 = \u2212dc}, BE12 = {(\u03b1, tc) \u2208 R2 : \u03b1 = dc}. 4 M. JIA, Y. SU, H. CHEN EJDE-2023/83 (b) Homoclinic bifurcation curves: HL11 = {(\u03b1, tc) \u2208 R2 : \u2212dc < \u03b1 \u2264 dc, tc = \u03c6(\u03b1)}, HL12 = {(\u03b1, tc) \u2208 R2 : \u03b1 > dc, tc = \u03d5(\u03b1)}. (c) Double limit cycle bifurcation curve: DL1 = {(\u03b1, tc) \u2208 R2 : \u03b1 > dc, tc = h(\u03b1)}, where the function tc = \u03c6(\u03b1) is continuous, monotonic and satisfies max{t\u2217c ,\u22122 \u221a dc} < \u03c6(\u03b1) < 0 for \u2212 dc < \u03b1 < dc, max{t\u2217c ,\u22122 \u221a dc} < \u03c6(\u03b1) < < \u03b1 < \u03b1\u2217 < dc, tc = \u03c6(\u03b1)}, HL112 = {(\u03b1, tc) \u2208 R2 : \u2212dc", "mime": "application/pdf"}, {"id": "ejde-573", "words": "6647", "extension": ".pdf", "flesch": "87", "author": "Li, Yang; Chen, Guiling", "title": "Existence of periodic solutions and stability for a nonlinear system of neutral differential equations", "date": "2024", "keywords": "s\u2212\u03c41(s; t\u2212\u03c41(t; x(t\u2212; \u2212 \u222b; \u222b t", "summary": "\u222b t 0 K\u22121(s) +G(s, x(s), x(s\u2212 \u03c42(s)))] ds + \u222b t 0 K\u22121(T )K\u22121(s)A(s)", "mime": "application/pdf"}, {"id": "ejde-575", "words": "10109", "extension": ".pdf", "flesch": "88", "author": "Tu, Jin; Wei, Huizhen", "title": "Form of solutions to quadratic trinomial partial differential equations with two complex variables", "date": "2024", "keywords": "+ \u221a; b21; \u2212a2 +", "summary": "Similarly, we obtain f(t, s) = \u222b t 0 [ \u03b12k1 2 \u221a 2(1 + \u03b1) + (\u03b12 + 4)k2 2 \u221a 2(1\u2212 \u03b1) ] eg(z)/2dt+ \u03d50(s), (5.14) where \u03d50(s) is a finite order transcendental entire function in s = z2 \u2212 z1. Similarly, we obtain f(t, s) = \u222b t 0 1\u221a 2 [ (A1 \u2212A2 +A1B12)e (B11+B12)t+B12s+\u03b21 + (A2 \u2212A1 +A2B22)e (B21+B22)t+B22s+\u03b22 ] dt+ \u03d50(s), (5.28) where \u03d50(s) is a transcendental entire function with finite order in s = z2 \u2212 z1.", "mime": "application/pdf"}, {"id": "ejde-58", "words": "5251", "extension": ".pdf", "flesch": "83", "author": "Jia, Xiaobiao; Ma, Shanshan", "title": "Holder estimates and asymptotic behavior for degenerate elliptic equations in the half space", "date": "2023", "keywords": "|x\u2032|2; \u03b2x2", "summary": "\u2212 z|1+\u03b1 \u2264 d\u03b1(y, z) \u2264 C|y \u2212 z|, (2.1) d\u03b1(y, z) \u223c |y \u2212 z| if y, z \u2208 B+ 1 \u2229 { xn \u2265 1 8 } . ,\u2223\u2223\u2223u( 1 2k h 1 2(1+\u03b1) en ) \u2212 u ( 1 2k+1 h 1 2(1+\u03b1) en )\u2223\u2223\u2223 \u2264 C2\u2212k\u22121h 1 2(1+\u03b1) , This implies that\u2223\u2223u( 1 2h 1 2(1+\u03b1) en ) \u2212 u(0) \u2223\u2223 h 1 2(1+\u03b1) \u2264 \u221e\u2211 k=1 \u2223\u2223u( 1 2k h 1 2(1+\u03b1) en )", "mime": "application/pdf"}, {"id": "ejde-580", "words": "15806", "extension": ".pdf", "flesch": "82", "author": "Avila, Jake; Cabarrubias, Bituin", "title": "Periodic unfolding method for domains with very small inclusions", "date": "2023", "keywords": "t \u03b4; theorem", "summary": "| u\u03b4,\u03b51 \u2208 V \u03b4,\u03b5p , u\u03b4,\u03b52 \u2208W 1,p(\u2126\u03b4,\u03b52 ) } , (3.4) equipped with the norm, \u2016u\u03b4,\u03b5\u2016p H\u03b4,\u03b5\u03b3,p = \u2016\u2207u\u03b4,\u03b51 \u2016 p Lp(\u2126\u03b4,\u03b51 ) + \u2016\u2207u\u03b4,\u03b52 \u2016 p Lp(\u2126\u03b4,\u03b52 ) + \u03b5\u03b3\u2016u\u03b4,\u03b51 \u2212 u \u03b4,\u03b5 2 \u2016 p Lp(\u0393\u03b4,\u03b5) . Then there exists a subsequence (still denoted by \u03b5), u1 \u2208 H1 0 (\u2126) and u\u03021 \u2208 L2(\u2126;H1 per(Y1)) such that T \u03b51 (u\u03b51)\u2192 u1 strongly in L2(\u2126;H1(Y1)), (2.2) T \u03b51 (\u2207u\u03b51) \u21c0 \u2207u1 +\u2207yu\u03021 weakly in L2(\u2126\u00d7 Y1), (2.3) with M\u0393(u\u03021) = 0 for almost every x", "mime": "application/pdf"}, {"id": "ejde-581", "words": "12504", "extension": ".pdf", "flesch": "82", "author": "Wu, Wanping; Zhang, Yinghui", "title": "Global low-energy weak solutions for compressible magneto-micropolar fluids with discontinuous initial data in R^3", "date": "2023", "keywords": "dxds; energy; q\u22122; solutions; sup; \u2212 \u222b; \u222b r3; \u222b t; \u222b t1", "summary": "= sup 1\u2264s\u2264t ( \u2016\u2207u\u20162L2 + \u2016w\u20162L2 + \u2016\u2207w\u20162L2 + \u2016\u2207H\u20162L2 ) + sup 1\u2264s\u2264t ( \u2016u\u0307\u20162L2 + \u2016w\u0307\u20162L2 + \u2016\u2207W1\u20162L2 + \u2016\u2207W2\u20162L2 + \u2016Ht\u20162L2 ) + \u222b t 1 ( \u2016u\u0307\u20162L2 + \u2016w\u0307\u20162L2 + \u2016\u2207W1\u20162L2 + \u2016\u2207W2\u20162L2 + \u2016Ht\u20162L2 ) ds + \u222b t 1 (\u2016\u2207u\u0307\u20162L2 + \u2016\u2207w\u0307\u20162L2 + \u2016\u2207Ht\u20162L2) ds, (3.3) Oq(t) = sup 0\u2264s\u2264t (\u2016u\u2016qLq + \u2016w\u2016qLq + \u2016H\u2016qLq ) + \u222b t 0 \u222b R3 ( |u|q\u22122|\u2207u|2 + |w|q\u22122|\u2207w|2 + |H|q\u22122|\u2207H|2 ) dxds + \u222b t 0 \u222b R3 ( |u|q\u22124|\u2207(|u|2)|2 + |w|q\u22124|\u2207(|w|2)|2 + |H|q\u22124|\u2207(|H|2)|2 ) Later, to deal with the terms 2\u03b6 \u222b t 0 \u222b R3 \u03d1 rotw \u00b7 u\u0307dx ds and 2\u03b6 \u222b t 0 \u222b R3 \u03d1 rotu \u00b7w\u0307 dxds, we use integration by parts to obtain 2\u03b6 \u222b t 0 \u222b R3 \u03d1 rotw \u00b7 u\u0307dxds+ 2\u03b6 \u222b t 0 \u222b R3 \u03d1 rotu \u00b7", "mime": "application/pdf"}, {"id": "ejde-587", "words": "16392", "extension": ".pdf", "flesch": "81", "author": "Hao, Jianghao; Wang, Dingkun", "title": "Asymptotic stabilization for Bresse transmission systems with fractional damping", "date": "2023", "keywords": "+ 4\u03b8; c\u2016e; e\u03b1\u2217; system; \u03c8\u0303\u20162; \u03d5\u0303\u20162; \u2016f\u20162; \u2016f\u2016\u2016u\u2016+", "summary": "The system is written as \u03c11\u03d5tt \u2212 \u03ba(\u03d5x + \u03c8 + lw)x \u2212 \u03ba0l(wx \u2212 l\u03d5) + \u03b31(\u2212\u2202xx)\u03b8\u03d5t = 0 in (0, L)\u00d7 R+, \u03c12\u03c8tt [40] got that when there are two locally distributed feedbacks on the shear angular displacement and longitudinal displacement, \u03c11\u03d5tt \u2212 \u03ba(\u03d5x + \u03c8 + lw)x \u2212 \u03ba0l(wx \u2212 l\u03d5) = 0 in (0, L)\u00d7 R+, \u03c12\u03c8tt", "mime": "application/pdf"}, {"id": "ejde-589", "words": "6682", "extension": ".pdf", "flesch": "78", "author": "Lu, Shuaishuai; Yang, Xue", "title": "Stability and rate of decay for solutions to stochastic differential equations with Markov switching", "date": "2024", "keywords": "decay; stability; x(t", "summary": "= 4k22t \u2227 4k23t, we obtain \u2016Vx(x, t, i)g(x, t, i)\u20162 \u2265 h2(t)V 2(x, t, i) for all i \u2208 {1, 2}. Therefore, (2.1) can be rewritten as the result of the following N equations: dx(t) = f(x(t), t, i)dt+ g(x(t), t, i)dW (t), t \u2265 0, 1 \u2264 i \u2264 N. (2.2)", "mime": "application/pdf"}, {"id": "ejde-59", "words": "5802", "extension": ".pdf", "flesch": "79", "author": "Chen, Ye-Jun; Ding, Hui-Sheng", "title": "Pseudo almost periodicity for stochastic differential equations in infinite dimensions", "date": "2023", "keywords": "periodic; pseudo; stochastic", "summary": "A family of measurable mappings on the sample space, \u03b8t : \u2126\u2192 \u2126, t \u2208 R, is called a measurable dynamical system if the following conditions are satisfied: Let X : R\u00d7 \u2126\u2192 B be a \u03b8p-almost periodic random process, and let J be a compact interval of R. Then (i) the set LJ = {X (s+ t, \u03b8\u2212t\u00b7) : s \u2208 J, t \u2208 R} is relatively compact in Lp(\u2126,B), (ii) the set S = {law(X(t, \u00b7)) : t \u2208 R} is uniformly tight, that is, for each \u03b5 > 0, there exists a compact subset K of B such that sup t\u2208R P ({\u03c9 \u2208 \u2126 : X(t, \u03c9) /\u2208", "mime": "application/pdf"}, {"id": "ejde-590", "words": "8376", "extension": ".pdf", "flesch": "79", "author": "Lou, Zhaowei; Wu, Youchao", "title": "A KAM theorem for degenerate infinite-dimensional reversible systems", "date": "2024", "keywords": "d(s; field; kam; lemma; systems; vector", "summary": "The map \u03a6 = \u03a6tF |t=1 defined above transforms X into X+ = \u03a6\u2217X = N+ + P+ on D(s\u2212 5\u03c3, \u03b7r), where N+ = N + N\u0302 , P+ = (\u03a61 F )\u2217(P \u2212R) + \u222b 1 0 (\u03a6tF )\u2217[R(t), F ]dt, with R(t) \u2212 i\u2126(\u03be)z\u0304 \u2202 \u2202z\u0304 , (5.13) P = \u2211 w\u2208{\u03b8,I,z,z\u0304} Pw(\u03b8, I, z, z\u0304; \u03be) \u2202 \u2202w (5.14) with \u03c9b = \u03bbjb \u2212 1 4 n\u2211 k=1 \u03bb\u22121 jk ajkjkjbjb\u03bek, \u2126j = \u03bbj \u2212 1 4 n\u2211 k=1 \u03bb\u22121 jk ajkjkjj\u03bek (5.15) P (\u03b8b) = \u22121 4 n\u2211 k=1 \u03bb\u22121 jk ajkjkjbjbIk \u2212 1 4 \u2211 l\u2208N1 \u03bb\u22121 l alljbjb |zl|2 + (Q\u0302(qjb ) +K(qjb ))", "mime": "application/pdf"}, {"id": "ejde-592", "words": "12889", "extension": ".pdf", "flesch": "75", "author": "Diaz, Jesus Ildefonso; Shaposhnikova, Tatiana A.; Podolskiy, Alexander V.", "title": "Strange non-local operators homogenizing the Poisson equation with dynamical unilateral boundary conditions: asymmetric particles of critical size", "date": "2024", "keywords": "\\gj \u03b5; j \u03b5; j \u03b5/4; l2(0; problem; t j; \u03b4 \u03b5; \u03b5\u2212\u03b3 \u222b; \u222b t; \u222b \u2202gj", "summary": "and we have \u03b5\u2212\u03b3 \u222b T 0 \u222b S\u03b5 \u2202tu\u03b5(\u03c6\u2212 u\u03b5) ds dt+ \u222b T 0 \u222b \u2126\u03b5 \u2207u\u03b5\u2207(\u03c6\u2212 u\u03b5) ds dt = \u222b T 0 \u222b \u2126\u03b5 f(\u03c6\u2212 u\u03b4\u03b5) dx dt.", "mime": "application/pdf"}, {"id": "ejde-593", "words": "9037", "extension": ".pdf", "flesch": "88", "author": "Xu, Hong Yan; Haldar, Goutam", "title": "Entire solutions to Fermat-type difference and partial differential-difference equations in C^n: System of Fermat-type difference equations in $ \\mathbb{C}^n $", "date": "2024", "keywords": "difference; equations; fermat; ia2; p1(z; type", "summary": "\u2212 ( ia3e \u2212ik \u2212 a1 ) e\u2212ike2ip1(z) = a1e \u2212ik + ia3. (3.26) Let us choose a1 = a2 = a3 = 1, a4 = \u22121, L(z) = i(z1 \u2212 z2), \u03a6(t) = i(c2z1\u2212c1z2) 5, A = 3, and c = (c1, c2) \u2208 C2 such that c1+2c2 = (2m\u22121/2)\u03c0, m being an integer.", "mime": "application/pdf"}, {"id": "ejde-594", "words": "10909", "extension": ".pdf", "flesch": "89", "author": "Li, Yuequn; Liu, Hui; Guo, Fei", "title": "Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion", "date": "2024", "keywords": "a(yes/2; b2(t(s; d\u03b1(s; e\u2212s; lemma; proof; solution; \u222b r", "summary": "(4.9) Substituting (4.7) into (3.3) gives fs \u2212 y 2 fy \u2212 1 2 f = g, s > 0, y \u2208 R, e\u2212s b2(t(s)) (gs \u2212 3 2 g \u2212 y 2 gy) + g = (a(yes/2)fy)y + \u03b1(s)(a0(yes/2)\u03d5\u20320(y))y + h(s, y), s > 0, y \u2208 R, f(0, y) = v(0, y)\u2212 \u03b1(0)\u03d50(y), y \u2208 R, g(0, y) = w(0, y)\u2212 \u03b1\u0307(0)\u03d50(y)\u2212 \u03b1(0)\u03c80(y), y \u2208 R, (4.10) where h(s, y) = e\u2212s b2(t(s)) ( \u22122\u03b1\u0307(s)\u03c80(y) + \u03b1(s)( y 2 \u03c8\u20320(y) + 3 2 \u03c80(y)) ) + r(s, y)\u2212 \u03d50(y) \u222b R r(s, y)dy, (4.11) here we have used (4.5) and a(x) = a\u0303(x) + a0(x).", "mime": "application/pdf"}, {"id": "ejde-596", "words": "6698", "extension": ".pdf", "flesch": "76", "author": "Calamai, Alessandro; Spadini, Marco", "title": "Caratheodory periodic perturbations of degenerate systems", "date": "2024", "keywords": "set", "summary": "We concentrate on the family of systems where the constraining manifold is of the form M = M \u00d7 N , the cartesian product of two smooth boundaryless manifolds M \u2286 Rk and N \u2286 Rs, and G : M \u00d7N \u2192 Rk \u00d7Rs is of the form (0, g), i.e., the first component is identically zero and g : Moreover, by the assumptions on the sequences {fn}, {gn}, {hn} we have, for a.a. t \u2208", "mime": "application/pdf"}, {"id": "ejde-597", "words": "10169", "extension": ".pdf", "flesch": "88", "author": "Osawa, Satoshi; Takaoka, Hideo", "title": "Global well-posedness for Cauchy problems of Zakharov-Kuznetsov equations on cylindrical spaces", "date": "2024", "keywords": "case; equation; ql2", "summary": "| |\u03be| \u223c K, |(\u03be1, q1)| \u2208 IN1 , |(\u03be \u2212 \u03be1, q \u2212 q1)| \u2208 IN2 , |\u03c41 \u2212 \u03c3(\u03be1, q1)| \u2208 IL1 , |\u03c4 \u2212 \u03c41 \u2212 \u03c3(\u03be \u2212 \u03be1, q \u2212 q1)| \u2208 IL2 } . Here \u0393\u03be1,q1,\u03c41\u03be,q,\u03c4 = |\u03be|\u3008\u03b6\u3009 \u3008\u03b61\u3009\u3008\u03b6 \u2212 \u03b61\u3009\u3008\u03c4 \u2212 \u03c3(\u03b6)\u30091/2\u2212\u3008\u03c41 \u2212 \u03c3(\u03b61)\u30091/2+\u3008\u03c4 \u2212 \u03c41 \u2212 \u03c3(\u03b6 \u2212 \u03b61)\u30091/2+ .", "mime": "application/pdf"}, {"id": "ejde-598", "words": "6193", "extension": ".pdf", "flesch": "89", "author": "Iaia, Joseph", "title": "Existence of two infinite families of solutions for singular superlinear equations on exterior domains", "date": "2024", "keywords": "m1,a", "summary": "(2.47) 10 J. IAIA EJDE-2024/06 Evaluating (2.47) at t = R1+M1,a 2 we see v1\u2212pa (R1 +M1,a 2 ) \u2265 (p\u2212 1)f4R \u2212\u03b1\u03031 1 2 (R1 \u2212M1,a 2 )2 and therefore vp\u22121a (R1 +M1,a 2 ) (2.48) By (2.45) we see then for large a that va (R1 +M1,a 2 ) \u2264 ( 32R\u03b1\u03031\u22122 1 (p\u2212 1)f4 ) 1 p\u22121 .", "mime": "application/pdf"}, {"id": "ejde-6", "words": "10059", "extension": ".pdf", "flesch": "82", "author": "Yu, Xiu-Fang; Wang, Jun-Min; Zhang, Han-Wen", "title": "Internal stabilization of interconnected heat-wave equations", "date": "2023", "keywords": "heat; sinh; system; wave; \u03b7 0; \u03be \u03b7; \u222b \u03b7", "summary": "\u03b7 0 |Gn\u03be (\u03be, s)|ds+ |a|d \u222b \u03b7 0 |Hn \u03be (\u03be, s)|ds \u2264 ( |a| 2 + |a|d ) MKn (n+ 1)! (\u03be + \u03b7)n+1 \u2264 ( |a| 2 + |a|d )MKn n! (\u03be + \u03b7)n, |Hn+1 \u03b7\u03b7 (\u03be, \u03b7)| \u2264 |a| 2 \u222b \u03be 0 |Gn\u03b7 (\u03c4, \u03b7)|d\u03c4 + |a|d \u222b \u03be 0 |Hn \u03b7 (\u03c4, \u03b7)|d\u03c4 \u2264 ( |a| 2 + |a|d )MKn n! (\u03be + \u03b7)n, and |Gn+1(\u03be, \u03b7)| \u2264 \u03b12 4 \u222b \u03be \u03b7 \u222b \u03b7 0 |Gn(\u03c4, s)| ds d\u03c4 + |a| 2 \u222b \u03be \u03b7 \u222b \u03b7 0 |Hn \u03be\u03be(\u03c4, s)| ds d\u03c4 + |a| \u222b \u03be \u03b7 \u222b \u03b7 0 |Hn \u03be\u03b7(\u03c4, s)| ds d\u03c4 + |a| 2 \u222b \u03be \u03b7 \u222b \u03b7 0 |Hn \u03b7\u03b7(\u03c4, s)| ds d\u03c4 \u2264 \u03b12 4 MKn n! \u222b \u03be \u03b7 \u222b \u03b7 0 (\u03c4 + s)n ds d\u03c4 + 2|a|MKn (n\u2212 1)! \u222b \u03be \u03b7 \u222b \u03b7 0 (\u03c4 + s)n\u22121 ds d\u03c4 = \u03b12 4 MKn (n+ 1)! \u222b \u03be \u03b7 [(\u03c4 + \u03b7)n+1 \u2212 \u03c4n+1]d\u03c4 According to boundary conditions of the last line in (3.7), we obtain c1 + c2 = 0, c3 + c4 = 0, e \u221a \u03bbc1 + e\u2212 \u221a \u03bbc2 \u2212 p\u03bbe\u03bb+\u03b1c3 \u2212 p\u03bbe\u2212(\u03bb+\u03b1)c4 = 0, p \u221a \u03bbe \u221a \u03bbc1", "mime": "application/pdf"}, {"id": "ejde-60", "words": "7818", "extension": ".pdf", "flesch": "80", "author": "Clark, Jason; Misiats, Oleksandr; Mogylova, Viktoriia; Stanzhytskyi, Oleksandr", "title": "Asymptotic behavior of stochastic functional differential evolution equation", "date": "2023", "keywords": "b\u03c10; differential; equations; theorem", "summary": "dt \u2264 C2 \u222b T 0 dt \u222b t 0 ( 1 + E\u2016\u03a6s\u2016pB\u03c11 ) ds \u2264 C3 + C2 \u222b T 0 \u222b t 0 E (\u222b 0 \u2212h \u2016\u03a6(s+ \u03b8, \u00b7)\u20162B\u03c10 d\u03b8 )p/2 ds dt \u2264 C3 + C4E \u222b T \u2212h \u2016\u03a6(t, \u00b7)\u2016p B\u03c10 dt <\u221e. (3.2) To estimate I3, we use [9, Lemma 7.2] and (2.10). EJDE-2023/35 STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS 11 I4 \u2264 Cp\u03c1 (T )Lp \u222b t 0 E (\u222b s 0 \u2016\u03a6\u03c4 (\u00b7)\u2212 \u03a6\u0303\u03c4 (\u00b7)\u2016B\u03c11 d\u03c4 )p ds \u2264 C(\u03c1, T, p) \u222b t 0 \u222b", "mime": "application/pdf"}, {"id": "ejde-600", "words": "7400", "extension": ".pdf", "flesch": "75", "author": "Belinskiy, Boris P.; Smith, Tanner A.", "title": "Optimal mass of structure with motion described by Sturm-Liouville operator: design and predesign", "date": "2024", "keywords": "conditions; mass; problem; q(s; sinh(2", "summary": "Finally, we introduce a set of solvability conditions on the S-L problem data, confirming that the corre- sponding critical points represent meaningful solutions we refer to as designs. \u2212 2 (\u222b 1 0 q(x) sin2( \u221a |\u03bb1|g(x) + z\u2032)dx\u2212 \u03c6 sin2(z\u2032) )] , (3.6) subject to solvability conditions which we omit here.", "mime": "application/pdf"}, {"id": "ejde-602", "words": "5036", "extension": ".pdf", "flesch": "75", "author": "Motreanu, Dumitru; Tornatore, Elisabetta", "title": "Dirichlet problems with anisotropic principal part involving unbounded coefficients", "date": "2024", "keywords": "problem", "summary": ". , N , and a Carathe\u0301odory function F : \u2126 \u00d7 R \u00d7 RN \u2192 R (i.e., F (\u00b7, t, \u03be) is measurable on \u2126 for each (t, \u03be) \u2208 R\u00d7RN and F (x, \u00b7, \u00b7) is continuous on R \u00d7 RN for almost all x \u2208 \u2126). , pN ) and denote by W 1,\u2212\u2192p 0 (\u2126) the completion of the set of smooth functions with compact support C\u221ec (\u2126) with respect to the norm \u2016u\u2016 := N\u2211 i=1 \u2016\u2202iu\u2016Lpi .", "mime": "application/pdf"}, {"id": "ejde-604", "words": "8077", "extension": ".pdf", "flesch": "75", "author": "Zhang, Guoping; Aburamyah, Ghder", "title": "Global attractor and l^p solutions to initial value problems of discrete nonlinear Schrodinger equations complex potential", "date": "2024", "keywords": "n\u2208zd; p\u03b8(zd; solution; u(t", "summary": "By Theorem 4.2, if u0 \u2208 u0 \u2208 D\u0398\u2229B, then u(t) = S(t)u0 is a global classical solution of the initial value problem (1.1)-(1.2). [19] A. Pankov, G. Zhang; Standing wave solutions for discrete nonlinear Schro\u0308dinger equations with unbounded potentials and saturable nonlinearities, J. Math.", "mime": "application/pdf"}, {"id": "ejde-605", "words": "6850", "extension": ".pdf", "flesch": "82", "author": "Boccardo, Lucio; Diaz, Jesus Ildefonso; Gomez-Castro, David", "title": "Failure of the Hopf-Oleinik lemma for a linear elliptic problem with singular convection of non-negative divergence", "date": "2024", "keywords": "theorem", "summary": "We focus our efforts on the particular case E = \u2212\u03d5\u22121\u2212\u03b3 1 \u2207\u03d51, for some \u03b3 > 0, (6.1) and f \u2208 L\u221ec (\u2126), the space of bounded functions with compact support in \u2126. The aim of this section is to prove the following theorem. Let E be given by (6.1), M = I and f \u2208 L\u221ec (\u2126).", "mime": "application/pdf"}, {"id": "ejde-606", "words": "6050", "extension": ".pdf", "flesch": "82", "author": "Severo, Uberlandio B.; Ribeiro, Bruno H. C.; Germano, Diogo de S.", "title": "Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity", "date": "2024", "keywords": "equations; lemma", "summary": "Introduction and main result In this work we consider the quasilinear equation \u2212 div(g2(u)\u2207u) + g(u)g\u2032(u)|\u2207u|2 + V (x)u = f(x, u) + \u03bb|u|p\u22122u+ h(x)g(u) (1.1) in R2, where g : R \u2192 R+ is a function of class C1, V : R2 \u2192 R is a potential that can change sign, f : R2 \u00d7 R \u2192 R is a measurable function, which may have exponential critical growth of Trudinger-Moser type, \u03bb \u2208 R is a parameter, p \u2265 2 and h \u2208 Lq(R2) for some 1 < q \u2264 2. When g(s) \u2261 1 and \u03bb = 0, equation (1.1) becomes the nonhomogeneous semilin- ear Schro\u0308dinger equation \u2212\u2206u+ V (x)u = f(x, u) + h(x) in R2, (1.2) which has been studied by several researchers, see for example", "mime": "application/pdf"}, {"id": "ejde-608", "words": "6972", "extension": ".pdf", "flesch": "87", "author": "Ding, Yuanlin; Liu, Kui", "title": "Properties of the solutions to periodic conformable non-autonomous non-instantaneous impulsive differential equations", "date": "2024", "keywords": "pl)\u03c6(tl; s\u03c2(c; \u03bb(t; \u03c2(c", "summary": "= \u03b4l(t)\u03b2(t + l ), t \u2208 (tl, sl], l \u2208 N, \u03b2(s+l ) = (E+ Pl)\u03b2(t \u2212 l ) +Ql, l \u2208 N := {1, 2, . . . }, \u03b2(t) = \u03b4l(t)\u03b2(t + l ), t \u2208 (tl, sl], l \u2208 N, \u03b2(s+l )", "mime": "application/pdf"}, {"id": "ejde-609", "words": "8696", "extension": ".pdf", "flesch": "83", "author": "Munoz Rivera, Jaime E.; Baldez, Carlos A. da Costa; Cordeiro, Sebastiao M. S.", "title": "Signorini's problem for the Bresse beam model with localized Kelvin-Voigt dissipation", "date": "2024", "keywords": "ejde-2024/17; l2(0; problem", "summary": "\u2212 \u03ba0(\u03b6x \u2212 lv)x \u2212 lK(\u03b6xt \u2212 lvt)x + l\u03ba(vx + y + l\u03b6) + lK(vxt + yt + l\u03b6t) = 0. (4.6) EJDE-2024/17 SIGNORINI\u2019S PROBLEM FOR BRESSE BEAMS 15 Multiplying (4.4) by vt, (4.5) by wt, and integrating over [0, `], we obtain d dt \u2016Um(t)\u20162H + \u222b ` `0 K|vxt + yt + l\u03b6t|2 +B|yxt|2 +K|\u03b6xt \u2212 lvt|2 dx+ \u03b5|ut|2 + \u03b5|zt|2 = \u2212S\u0303m(`\u22120 , t)\u03d5t(` \u2212 0 , t)\u2212 M\u0303m(`\u22120 , t)\u03c8t(` \u2212 0 , t)\u2212 N\u0303m(`\u22120 , t)wt(` \u2212 0 , t) (4.7) where Um(t) = \u2212 byxx \u2212 (Byxt)x + \u03ba(vx + y + l\u03b6) +K(vxt + yt + l\u03b6t) = 0, (4.5) \u03c11\u03b6tt", "mime": "application/pdf"}, {"id": "ejde-61", "words": "7818", "extension": ".pdf", "flesch": "80", "author": "Li, Sheng-Jie; Chai, Shugen", "title": "Stabilization of semilinear wave equations with time-dependent variable coefficients and memory", "date": "2022", "keywords": "b\u03c10; differential; equations; theorem", "summary": "dt \u2264 C2 \u222b T 0 dt \u222b t 0 ( 1 + E\u2016\u03a6s\u2016pB\u03c11 ) ds \u2264 C3 + C2 \u222b T 0 \u222b t 0 E (\u222b 0 \u2212h \u2016\u03a6(s+ \u03b8, \u00b7)\u20162B\u03c10 d\u03b8 )p/2 ds dt \u2264 C3 + C4E \u222b T \u2212h \u2016\u03a6(t, \u00b7)\u2016p B\u03c10 dt <\u221e. (3.2) To estimate I3, we use [9, Lemma 7.2] and (2.10). EJDE-2023/35 STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS 11 I4 \u2264 Cp\u03c1 (T )Lp \u222b t 0 E (\u222b s 0 \u2016\u03a6\u03c4 (\u00b7)\u2212 \u03a6\u0303\u03c4 (\u00b7)\u2016B\u03c11 d\u03c4 )p ds \u2264 C(\u03c1, T, p) \u222b t 0 \u222b", "mime": "application/pdf"}, {"id": "ejde-610", "words": "4980", "extension": ".pdf", "flesch": "73", "author": "Wang, Lixia; Zhao, Pingping; Zhang, Dong", "title": "Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations", "date": "2024", "keywords": "klein", "summary": "By (1.3) and the Gateaux derivative of I, we can obtain that \u2016un \u2212 u\u20162 = \u3008I \u2032(un)\u2212 I \u2032(u), un \u2212 u\u3009+ V0 \u222b R3 (un \u2212 u)2 dx+ 2\u03c9 \u222b R3 (\u03c6unun \u2212 \u03c6uu)(un \u2212 u) dx + \u222b R3 (h(x, un)\u2212 h(x, u))(un \u2212 u) dx+ \u222b R3 (\u03c62 un un \u2212 \u03c62 uu)(un \u2212 u) dx By an easy computation, we obtain that \u3008 [(\u03c62 un un \u2212 \u03c62 uu)(un \u2212 u) dx \u2223\u2223 \u2264 |\u03c62 un un \u2212 \u03c62 uu|3/2|un \u2212 u|3 \u2264 (|\u03c62 un un|3/2 + |\u03c62 uu|3/2)|un \u2212 u|3 \u2192 0, as n\u2192 +\u221e. By Proposition 2.3 and un \u2192 u in Ls(R3) for 2 \u2264 s < 6, we have\u222b R3 (h(x, un)\u2212 h(x, u))(un \u2212 u)", "mime": "application/pdf"}, {"id": "ejde-611", "words": "14055", "extension": ".pdf", "flesch": "91", "author": "Zhang, Bo; Zhang, Wei", "title": "Localized nodal solutions for semiclassical Choquard equations with critical growth", "date": "2024", "keywords": "2\u2217\u03b1; b(y; choquard; dx dy; equations; lemma; rn \u03c7\u03b5(x)u2; solutions; y|\u03b1; y|\u03b1 dx; zhang; |x\u2212; \u222b rn", "summary": "In this article, we study the existence of localized nodal solutions for semiclassical Choquard equation with critical growth \u2212\u03b52\u2206v + V (x)v = \u03b5\u03b1\u2212N (\u222b RN |v(y)|2\u2217\u03b1 |x\u2212 y|\u03b1 dy ) |v|2 \u2217 \u03b1\u22122v + \u03d1|v|q\u22122v, x \u2208 RN , where \u03d1 > 0, N \u2265 3, 0 < Introduction In this article, we study localized nodal solutions of the nonlinear Choquard equation with critical exponent \u2212\u03b52\u2206v + V (x)v = \u03b5\u03b1\u2212N (\u222b RN |v(y)|2\u2217\u03b1 |x\u2212 y|\u03b1 dy ) |v|2 \u2217 \u03b1\u22122v + \u03d1|v|q\u22122v, x \u2208 RN , v(x)\u2192 0 as |x| \u2192 \u221e, (1.1) where \u03d1 > 0, N \u2265 3, 0 <", "mime": "application/pdf"}, {"id": "ejde-615", "words": "6758", "extension": ".pdf", "flesch": "85", "author": "Zhang, Jichao; Bu, Shangquan", "title": "Maximal regularity for fractional difference equations of order 2", "date": "2024", "keywords": "regularity", "summary": "\u2212 1)\u03b1[z1\u2212\u03b1(z \u2212 1)\u03b1 \u2212 T ]\u22121 : |z| = 1, z \u0338= 1 } is R-bounded [18]. In the case 1 < \u03b1 \u2264 2, 1 < p < \u221e and X is a UMD space, Lizama and Arcila showed that (1.1) with the initial conditions u(0) = u(1) = 0, has the \u2113p-maximal regularity if and only if {z2\u2212\u03b1(z \u2212 1)\u03b1 : |z| = 1, z \u0338= 1} \u2282 \u03c1(T ), and the set { z2\u2212\u03b1(z \u2212 1)\u03b1[z2\u2212\u03b1(z \u2212 1)\u03b1 \u2212 T ]\u22121 : |z| = 1, z \u0338= 1 } is R-bounded [19].", "mime": "application/pdf"}, {"id": "ejde-619", "words": "9204", "extension": ".pdf", "flesch": "83", "author": "Faria, Luiz F. O.; Montenegro, Marcelo", "title": "Positive solution for a nonlinear elliptic equation on symmetric domains", "date": "2024", "keywords": "1,p; 1,p(rn", "summary": "Then there exists \u03bb\u2217 > 0 such that for every \u03bb \u2208 (0, \u03bb\u2217) problem (1.14) possesses at least one positive radially symmetric solution u\u03bb \u2208 W 1,p 0 (RN\\BR). Let u \u2208 W 1,p 0,r (RN ) with \u2225u\u2225W 1,p(RN )", "mime": "application/pdf"}, {"id": "ejde-620", "words": "9826", "extension": ".pdf", "flesch": "80", "author": "Ayachi, Moez; Abbas, Syed", "title": "P-mean (mu1,mu2)-pseudo almost periodic processes and application to integro-differential stochastic evolution equations", "date": "2024", "keywords": "lp(p; mean; stochastic; \u00b51,2; \u222b +; \u222b t", "summary": "= U(t, a)Z(a) + \u222b t a U(t, s)F1(s, Z(s))ds + \u222b t a U(t, s) \u222b s a Q(s\u2212 \u03b6)F2(\u03b6, Z(\u03b6))d\u03b6ds + \u222b t a U(t, s) \u222b [Z(0)\u2212 Z\u2217(0)] + \u222b t 0 U(t, s)", "mime": "application/pdf"}, {"id": "ejde-622", "words": "6665", "extension": ".pdf", "flesch": "79", "author": "Gao, Yingchun; Liu, Kai; Qi, Xiaoguang", "title": "Crossed differential systems of equations and Clunie lemma", "date": "2024", "keywords": "differential; equations; f(z; g(z; s(r; solutions", "summary": "By the addition and subtraction of two equations in (3.6), we have ff \u2032+ gg\u2032 = 2\u2212 f \u2032\u2212 g\u2032 and ff \u2032\u2212 gg\u2032 = f \u2032\u2212 g\u2032. Integrating the above two equations, we have 1 2 f2 \u2212 1 2 g2 = f \u2212 g +A1, and 1 2 f2 + 1 2 g2 = 2z \u2212 f \u2212 g +A2, thus we have T (r, f) If L(z, f) = L(z, g) implies that f = g, where f(z) and g(z) are two meromorphic functions, then L(z, f) is called a unique differential polynomial of meromorphic functions (UDPM).", "mime": "application/pdf"}, {"id": "ejde-623", "words": "5147", "extension": ".pdf", "flesch": "82", "author": "Gao, Yue; Yang, Xue", "title": "Periodic solutions in distribution for stochastic lattice differential equations", "date": "2024", "keywords": "distribution; equations; l2\u03c1; periodic; solutions", "summary": "By Ho\u0308lder inequality, [20, Theorem 1.7.2], Assumption 2.1, and (3.1), we obtain E ( sup 0\u2264s\u2264t \u2225u(t)\u2225p\u03c1 ) = E ( sup 0\u2264s\u2264t \u2225u0 + \u222b s 0 [\u2212\u03bdAu(s)\u2212 \u03bbu(s) + f(u(s)) + g(r)]dr + \u222b s 0 \u03c3(r, u(r))dW (r)\u2225p\u03c1 ) \u2264 3p\u22121E\u2225u0\u2225p\u03c1 + (12t)p\u22121E[ \u222b t 0 \u2225 \u2212 \u03bdAu(s)\u2212 \u03bbu(s) + f(u(s)) = \u222b t 0 [\u2212\u03bdA(u(s)\u2212 u\u0303(s))\u2212 \u03bbu(s) + \u03bbu\u0303(s)) + f(u(s))\u2212 f(u\u0303(s))]ds+ \u222b t 0", "mime": "application/pdf"}, {"id": "ejde-624", "words": "8823", "extension": ".pdf", "flesch": "82", "author": "Webb, Jeffrey", "title": "Nonexistence results for fractional differential inequalities", "date": "2024", "keywords": "fractional; solution", "summary": "We can integrate from 1 to t \u2264 T to obtain g1\u2212p(t) \u2264 v1\u2212p 0 \u2212 (p\u2212 1) \u0393(\u03b1) (t1\u2212\u03b3 \u2212 1) 1\u2212 \u03b3 , for \u03b3 < 1, g1\u2212p(t) \u2264 v1\u2212p 0 \u2212 (p\u2212 1) \u0393(\u03b1) u \u2208 AC[0, T ] if and only if u\u2032 \u2208 L1[0, T ], u\u2032(t) exists for almost every (a.e.) t \u2208", "mime": "application/pdf"}, {"id": "ejde-627", "words": "2667", "extension": ".pdf", "flesch": "77", "author": "Alshanti, Waseem Ghazi", "title": "Solutions of linear and non-linear partial differential equations by means of tensor product theory of Banach space", "date": "2024", "keywords": "differential; equations; solution", "summary": "5. Conclusions This article has introduced a new analytical method for handling non-separable, linear and non-linear partial differential equations via atomic solutions method. Partial differential equations; tensor product of Banach spaces; atomic solution.", "mime": "application/pdf"}, {"id": "ejde-629", "words": "5339", "extension": ".pdf", "flesch": "77", "author": "Liu, Qiang; Zhu, Wanyu; Ye, Hailong", "title": "Mild solutions to fourth-order parabolic equations modeling thin film growth with time fractional derivative", "date": "2024", "keywords": "2\u2212\u03b2", "summary": "However, to the best of our knowledge, the well-posedness for the solutions of the time fractional thin film growth equation is not clear, which is the main motivation of the present work. Ct \u03b1\u03b3 4\u03b22 \u2212 \u03b1 2\u03b2 R(t)1+\u03b2 j , and similarly \u2225\u22072uj+1\u2225 \u03b2N 2\u2212\u03b2 \u2264 \u2225\u22072E\u03b1(\u2212t\u03b1A)\u03c6\u2225 \u03b2N 2\u2212\u03b2 + \u222b t 0 (t\u2212 s)\u03b1\u22121\u2225\u22072E\u03b1,\u03b1(\u2212(t\u2212 s)\u03b1A)\u2207 \u00b7 f(\u2207uj)\u2225 \u03b2N 2\u2212\u03b2 ds \u2264 \u2225\u22072u0\u2225 \u03b2N 2\u2212\u03b2 + C \u222b t 0 (t\u2212 s) \u03b1 2 \u22121\u2212\u03b1\u03b3 4\u03b2 \u2225\u2207 \u00b7 f(\u2207uj)\u2225 \u03b2N 2\u2212\u03b2+\u03b3 ds \u2264 \u2225\u22072u0\u2225 \u03b2N 2\u2212\u03b2 + CR(t)1+\u03b2 j \u222b t 0 (t\u2212 s) \u03b1 2 \u22121\u2212\u03b1\u03b3 4\u03b2 s\u2212\u03b1+\u03b1\u03b3 4\u03b2 ds (3.6) \u2264 \u2225\u22072u0\u2225 \u03b2N 2\u2212\u03b2 + Ct\u2212 \u03b1 2 R(t)1+\u03b2 j . Combining (3.5) and (3.6), for any fixed T > 0, we have R(T )j+1 \u2264 R(T )0 + CR(T )1+\u03b2 j , where C > 0 is independent of T .", "mime": "application/pdf"}, {"id": "ejde-636", "words": "9218", "extension": ".pdf", "flesch": "85", "author": "Ma, Zhouji; Chang, Xiaojun; Feng, Zhaosheng", "title": "Normalized ground state of a mixed dispersion nonlinear Schrodinger equation with combined power-type nonlinearities", "date": "2024", "keywords": "q(c", "summary": "= 1 2 \u2225\u2206u\u222522 + 1 2 \u2225\u2207u\u222522 \u2212 \u00b5 2 \u2225u\u2225qq \u2212 1 2 \u2225u\u2225pp = \u22121 2 \u03c9c, \u2202K \u2202t (1, 1) = \u2225\u2206u\u222522 + 1 2 \u2225\u2207u\u222522 \u2212 \u00b5\u03b3q\u2225u\u2225qq \u2212 \u03b3p\u2225u\u2225pp = 0, \u22022K \u2202t2 (1, 1) = \u2225\u2206u\u222522 \u2212 \u00b5\u03b3q( N(q \u2212 2) 4 \u2212 1)\u2225u\u2225qq \u2212 \u03b3p( N(p\u2212 2) 4 \u2212 1)\u2225u\u2225pp < 0, which yields for \u03b4t small enough and \u03b4\u03bb > 0, K(1 + \u03b4\u03bb, 1 + \u03b4t) < K(1, 1) for \u03c9 > 0. (4.8) + 1 2 \u2225\u2207u\u222522 \u2212 \u00b5\u03b3q\u2225u\u2225qq \u2212 \u03b3p\u2225u\u2225pp = 0.", "mime": "application/pdf"}, {"id": "ejde-637", "words": "11129", "extension": ".pdf", "flesch": "79", "author": "Han, Qian-Qian; Huan, Song-Mei", "title": "Global dynamics of a special class of planar sector-wise linear systems", "date": "2024", "keywords": "cycle; e =; linear; orbit; point; systems; x\u2212 e", "summary": "= \u22122 det(A) \u00b7 y+e \u00b7 (x\u2217 \u2212 x\u2212 e + x+ e 2 ) And by easy computation, we obtain that 2\u00b52 + x+ e \u2212 \u00b56 = \u03bb1 \u2212 \u03bb2 \u03bb1 \u2212 a11 x+ e + 2a12\u03bb1 a11(\u03bb1 \u2212 a11) y+e , which implies 2\u00b52 + x+ e < \u00b56 and 2\u00b52 + x+ e > \u00b56 both may be true.", "mime": "application/pdf"}, {"id": "ejde-64", "words": "7657", "extension": ".pdf", "flesch": "81", "author": "Liu, Zhenhai; Papageorgiou, Nikolaos S.", "title": "A weighted (p,2)-equation with double resonance", "date": "2023", "keywords": "1,p", "summary": "The reaction (right-hand side) of (1.1), is a Carathe\u0301odory function f(z, x) (that is, for all x \u2208 R, z \u2192 f(z, x) is measurable and for a.a.z \u2208 \u2126, x \u2192 f(z, x) is continuous) which exhibits (p \u2212 1) sublinear growth as x \u2192 \u00b1\u221e and resonance can occur with respect to the principal eigenvalue of (\u2212\u2206a1 p ,W 1,p 0 (\u2126)) EJDE-2023/30 A WEIGHTED (p, 2)-EQUATION WITH DOUBLE RESONANCE 13 Note that \u2207y\u03b3(z, y) = a1(z)|y|p\u22122[id+ (p\u2212 2) y \u2297 y |y|2 ] + a2(z)id \u2200z \u2208 \u2126, ;\u2200y \u2208 RN \u21d2 (\u2207y\u03b3(z, y)\u03b2, \u03b2)RN \u2265 c\u0302|\u03b2|2 for all y, \u03b2 \u2208 RN .", "mime": "application/pdf"}, {"id": "ejde-644", "words": "14190", "extension": ".pdf", "flesch": "87", "author": "Thorel, Alexandre", "title": "Solvability of transmission problems with generalized diffusion equation in L^p-spaces", "date": "2024", "keywords": "+ m; + m)2; + \u221a; ecm; k+(l+ +; r +; y +; z +", "summary": "edL+)\u03c81 \u2212 (I \u2212 edL+)\u03c82 + \u03c6\u0303+ 1 ] \u03b1+ 2 = \u2212 1 2r+ (L+ +M)U\u22121 + [ M(I + edM )\u03c81 \u2212 (I \u2212 edM )\u03c82 + \u03c6\u0303+ 2 ] \u03b1+ 3 = 1 2r+ (L+ +M)V \u22121 + [ L+(I \u2212 edL+)\u03c81 \u2212 (I + edL+)\u03c82 + \u03c6\u0303+ 3 ] \u03b1+ 4 = \u2212 1 2r+ (L+ +M)V \u22121 + [ M(I \u2212 edM )\u03c81 \u2212 (I + edM )\u03c82 + \u03c6\u0303+ 4 ] , (5.20) with \u03c6\u03031 + = \u2212L+ ( I + edL+ ) \u03c6+ 1 + ( I \u2212 edL+ ) ( F \u2032 +(b) + F \u2032 +(\u03b3)\u2212 \u03c6+ 2 ) \u03c6\u03032 + = \u2212M ( I + edM ) [ L+(I \u2212 edL+)\u03c81 \u2212 (I + edL+)\u03c82 + \u03c6\u0303+ 3 ] = 2M\u22121R2, Finally, using (5.2), (5.12), (5.13), (5.14) and (5.15), we obtain that the previous system writes as system (5.17).", "mime": "application/pdf"}, {"id": "ejde-647", "words": "8946", "extension": ".pdf", "flesch": "86", "author": "Jin, Lingyu; Wei, Suting", "title": "A global compactness result for quasilinear elliptic problems with critical\u00a0Sobolev nonlinearities and Hardy potentials on R^N", "date": "2024", "keywords": "1,p(rn; o(1; |x|p", "summary": "(A4) There exists a constant \u03b8 \u2208 (0, p\u2217 \u2212 p) such that t \u2202 \u2202tf(x, t) \u2a7e Moreover, we extend f(x, t) \u2261 0 for all t \u2208 (\u2212\u221e, 0), x \u2208 RN . (A3) There exists a constant q \u2208 (p, Np N\u2212p ) such that lim t\u2192+\u221e f(x,t) tq\u22121 = 0 and lim t\u21920+ f(x,t) tp\u22121 = 0 uniformly in x \u2208 RN .", "mime": "application/pdf"}, {"id": "ejde-649", "words": "12401", "extension": ".pdf", "flesch": "85", "author": "Caqui, Eduardo H.; Lima, Sandra M. de S.; Pereira, F\u00e1bio R.", "title": "Multiplicity results for critical fractional Ambrosetti-Prodi type system with nonlinearities interacting with the spectrum", "date": "2025", "keywords": "+ ut", "summary": "\u2212 U\u22252Y \u2212 (\u03b1+ \u03b2) \u222b \u2126 F (Un \u2212 U) dx+ \u222b \u2126 (\u2207F (U + UT ), UT )R2 dx + \u222b \u2126 (\u2207F (Un + UT ), UT )R2 dx+ o(1). Also (w, z) = ( (\u03bb1,s \u2212 c)t+ br det(\u03bb1,sI \u2212A) \u03d51,s, bt+ (\u03bb1,s \u2212 a)r det(\u03bb1,sI \u2212A) \u03d51,s ) is the unique solution of the system (\u2212 \u2212\u2192 \u2206)sU = AU + T\u03d51,s in \u2126, U = 0 in RN \\ \u2126. Consequently, if uT = (\u03bb1,s \u2212 c)t+ br det(\u03bb1,sI \u2212A) \u03d51,s + u0, vT = bt+ (\u03bb1,s \u2212 a)r det(\u03bb1,sI \u2212A) \u03d51,s + v0, then UT = (uT , vT ) is a solution of the system (\u2212 \u2212\u2192 \u2206)sU = AU + T\u03d51,s + F1 in \u2126, U = 0 in RN \\ \u2126. Clearly if uT and vT are negative in \u2126, we deduce also that UT is a solution of (1.2).", "mime": "application/pdf"}, {"id": "ejde-657", "words": "7168", "extension": ".pdf", "flesch": "81", "author": "Zhao, Fengxiang; Tang, Haotian; Zheng, Jiashan; Li, Kaiqiang", "title": "Existence and boundedness of solutions for a parabolic-parabolic\u00a0predator-prey model", "date": "2025", "keywords": "r1\u22121; r2 \u2212; r2\u22121; \u222b \u03c9", "summary": "To deal with u, multiplying both sides of the second equation in (1.1) by ur\u0303\u22121 and integrating by parts, for any small \u03b5 \u2208 (0, 1), we derive from Young\u2019s inequality that 1 r\u0303 d dt \u222b \u2126 ur\u0303 + (r\u0303 \u2212 1) \u222b \u2126 ur\u0303\u22122|\u2207u|2 = \u2212 r\u0303 \u2212 1 r\u0303 \u03c7 \u222b \u2126 ur\u0303\u2206w + \u03bb1 \u222b \u2126 ur\u0303 \u2212 \u00b51 \u222b \u2126 ur\u0303+r1\u22121 + a \u222b \u2126 ur\u0303v \u2264 r\u0303 \u2212 1 r\u0303 \u03ba \u222b \u2126 ur\u0303|\u2206w|+ \u03bb1 \u222b \u2126 ur\u0303 \u2212 \u00b51 \u222b \u2126 ur\u0303+r1\u22121 + \u03b5 \u222b \u2126 ur\u0303+r1\u22121 + C3 \u222b \u2126 v r\u0303+r1\u22121 r1\u22121 \u2200t \u2208 (0, Tmax), (3.29) where C3 = r\u0303 + r1 \u2212 1 r1 \u2212 1 (\u03b5 r\u0303 + r1 \u2212 1 r\u0303 )\u2212 r\u0303 r1\u22121 a r\u0303+r1\u22121 r1\u22121 . \u2212 r\u0303 r1\u22121 \u00d7 ( r\u0303 \u2212 1 r\u0303 \u03ba ) r\u0303+r1\u22121 r1\u22121 \u222b \u2126 |\u2206w| r\u0303+r1\u22121 r1\u22121 = \u03bb0 \u222b \u2126 ur\u0303+r1\u22121 + A\u03031\u03bb \u2212 r\u0303 r1\u22121 0 \u03ba r\u0303+r1\u22121 r1\u22121 \u222b \u2126 |\u2206w| r\u0303+r1\u22121 r1\u22121 \u2200t \u2208 (0, Tmax), (3.32) where A\u03031 = r1 \u2212 1 r\u0303 + r1 \u2212 1 ( r\u0303 + r1 \u2212 1 r\u0303 )\u2212 r\u0303 r1\u22121 ( r\u0303 \u2212 1 r\u0303 ) r\u0303+r1\u22121 r1\u22121 .", "mime": "application/pdf"}, {"id": "ejde-66", "words": "11989", "extension": ".pdf", "flesch": "83", "author": "Asso, Oumarou; Cuesta, Mabel; Doumate, Jonas Tele; Leadi, Liamidi", "title": "Principal eigenvalues for the fractional p-Laplacian with unbounded sign-changing weights", "date": "2023", "keywords": "eigenvalues; k(1\u2212; p(rn; p(\u03c9; w\u0303 s; \u03bb1(v", "summary": "Published June 19, 2023. 1 2 O. ASSO, M. CUESTA, J. T. DOUMATE\u0300, L. LEADI EJDE-2023/38 In this article, we study the conditions under which the principal eigenvalues of the following homogeneous Dirichlet problem exist (\u2212\u2206p) su+ V |u|p\u22122u = \u03bbm(x)|u|p\u22122u in \u2126, u = 0 in RN \\ \u2126, (1.1) where \u2126 is a bounded regular domain of RN , V and m are indefinite sign-changing functions and satisfying the following conditions: (C1) V , m \u2208 Lr(\u2126) with r \u2208 (1, +\u221e) \u2229 (Nsp , +\u221e), (C2) m+ = max(m, 0) 6\u2261 0. Let us consider the homogeneous problem (\u2212\u2206p) su+ V \u2032|u|p\u22122u = 0 in \u2126, u = 0 in RN \\ \u2126, (3.4) where V \u2032 satisfies condition (C1).", "mime": "application/pdf"}, {"id": "ejde-664", "words": "7870", "extension": ".pdf", "flesch": "84", "author": "Castillo, Ricardo; Guzman, Omar; Loayza, Miguel; Zegarra, Maria", "title": "Global solution for coupled parabolic systems with degenerate coefficients and time-weighted sources", "date": "2024", "keywords": "2\u2212\u03b1; \u03b3(x", "summary": "= \u222b RN \u0393(x, y, t)v0(y) dy + \u222b t 0 \u222b RN \u0393(x, y, t\u2212 \u03c3)h2(\u03c3)u(y, \u03c3) q dy d\u03c3 <\u221e, (1.5) for almost all x \u2208 RN and t \u2208 (0, T ). Suppose that (4.6) holds for some n \u2208 N. Then, by (2.2) we have \u2225un+1(t)\u2225\u221e \u2264 \u2225u1(t)\u2225\u221e + \u222b t 0 \u03c3r\u2225S(t\u2212 \u03c3)vn(\u03c3) p\u2225\u221e d\u03c3 \u2264 c1\u2225u0\u2225\u221e + c1 \u222b t 0 \u03c3r\u2225vn(\u03c3)\u2225p\u221e d\u03c3 \u2264 c1\u2225u0\u2225\u221e + c1[2c1(\u2225u0\u2225\u221e + \u2225v0\u2225\u221e)]p \u222b t 0 \u03c3r d\u03c3, (4.7) 14 R. CASTILLO, O. GUZMA\u0301N-REA, M. LOAYZA, M. ZEGARRA EJDE-2024/67 for t \u2208 (0, T ).", "mime": "application/pdf"}, {"id": "ejde-665", "words": "8006", "extension": ".pdf", "flesch": "84", "author": "Baig, Ayesha; Li , Zhouxin", "title": "Existence of positive solutions for systems of quasilinear Schrodinger equations", "date": "2025", "keywords": "lemma", "summary": "(1.8) where the functions W,V : RN \u2192 R are Ho\u0308lder continuous satisfying W (x), V (x) \u2265 \u03b1 > 0 in RN and the condition: (5) There exists an open and bounded set \u039b \u2282 RN , with x0 \u2208 \u039b and \u03c1 > 0, such that W (x), V (x) \u2265 \u03c1, for all x \u2208 \u2202\u039b and W (x0), V (x0) < Within this class of potentials, V satisfies (A1), (A2) and (A4) there exists a domain \u039b \u2282 RN where \u2207V (x) \u0338= 0 for all x \u2208 \u2202\u039b. Given that V falls into either Class 1 or Class 2 and taking into account certain conditions met by the nonlinearity, the author demonstrated the existence of a positive solution for \u03b5 > 0 sufficiently small. Alves", "mime": "application/pdf"}, {"id": "ejde-666", "words": "10506", "extension": ".pdf", "flesch": "77", "author": "Bandyopadhyay, Shalmali; Lewis, Thomas; Mavinga, Nsoki", "title": "Existence of maximal and minimal weak solutions and finite difference approximations for elliptic systems with nonlinear boundary conditions", "date": "2025", "keywords": "existence; f1(x; solutions", "summary": "\u2208 \u2202\u2126. Throughout this article we assume that each fi satisfies the quasimonotonicity condition (A1) the functions fi are quasimonotone nondecreasing in the sense that f1(x, u1, u2) is nonde- creasing in u2 for all fixed x \u2208 \u2202\u2126, u1 \u2208 R, and f2(x, u1, u2) is nondecreasing in u1 for all fixed x \u2208 \u2202\u2126, u2 \u2208 R. In this article, we establish the existence of maximal and minimal weak solutions for (1.1). We define the map T : J \u2192 (H1(\u2126))2 by T (U) =W , where J := {U = (u1, u2) \u2208 (H1(\u2126))2 : U \u2264 U \u2264 U} and W = (w1, w2) is the unique weak solution of the decoupled system \u2212\u2206wi + wi = 0 in \u2126; \u2202wi \u2202\u03b7 + kwi = fi(x, u1, u2) + kui on \u2202\u2126, i = 1, 2, (2.1) where k = k1 + k2 \u2265 0.", "mime": "application/pdf"}, {"id": "ejde-67", "words": "6665", "extension": ".pdf", "flesch": "73", "author": "El Attaouy, Meryem; Ezzinbi, Khalil; \u02dcN'Guerekata, Gaston Mandata", "title": "Reduction principle for partial functional differential equation without compactness", "date": "2023", "keywords": "function; periodic; semigroup; solution", "summary": "In this work we are interested in investigating the existence of almost automor- phic and almost periodic solutions for the partial functional differential equation x\u2032(t) = Ax(t) + L(xt) + f(t) for t \u2208 R, (1.3) whereA is the infinitesimal generator of a strongly continuous semigroup of bounded linear operators T (t) on a Banach space X. x(t) \u2208 X, L is a bounded linear opera- tor from C([\u2212r, 0], X) to X with C([\u2212r, 0], X) is the space of continuous functions from [\u2212r, 0] to X endowed with the uniform norm topology and r > 0. d\u03be ] (0), for t \u2208 R, is a mild solution of (1.3) on R. As a consequence of the above, we establish the following fundamental reduction principle which allows us to prove the existence of an almost automorphic and almost periodic solution of the (1.3).", "mime": "application/pdf"}, {"id": "ejde-673", "words": "13097", "extension": ".pdf", "flesch": "88", "author": "Aramaki, Junichi", "title": "Eigenvalue problems for Kirchhoff-type equations in variable exponent Sobolev spaces", "date": "2025", "keywords": "eigenvalue; function; proposition; space", "summary": "We say that a pair (u, \u03bb) \u2208 Y \u00d7 R is a weak solution of (1.1), if M (\u222b \u2126 A(x,\u2207u(x)) Let p \u2208 C+(\u2126) and let u, un \u2208 Y (n = 1, 2, . . .).", "mime": "application/pdf"}, {"id": "ejde-675", "words": "10740", "extension": ".pdf", "flesch": "88", "author": "Jiang, Qiaoyun; Li, Lin; Chen, Shangjie; Siciliano, Gaetano", "title": "Ground state solutions for the nonlinear Schr\u00f6dinger-Bopp-Podolsky systems with nonperiodic potentials", "date": "2024", "keywords": "lemma; on(1", "summary": "(ii) \u2225un \u2212 u\u2225ss = \u2225un\u2225ss \u2212 \u2225u\u2225ss + on(1), where s \u2208 (2, 6]. (iii) \u2225un \u2212 u\u2225s\u22122(un \u2212 u) = By a direct calculation, for p \u2208 [4, 6), J (un) = J (un)\u2212 1 4 \u27e8J \u2032(un), un\u27e9 = 1 4 \u2225un\u22252 + 1 12 \u222b |un|6 dx+ \u03bb( 1 4 \u2212 1 p ) \u222b |un|p dx \u2265 1 4 \u2225un\u22252.", "mime": "application/pdf"}, {"id": "ejde-681", "words": "4200", "extension": ".pdf", "flesch": "85", "author": "Silva, Joao Pablo Pinheiro da; Silva, Edcarlos Domingos da", "title": "Existence of semi-nodal solutions for elliptic systems related to Gross-Pitaevskii equations", "date": "2024", "keywords": "solutions", "summary": "= (un(\u03b4), vn(\u03b4)) by (u(\u03b4), v(\u03b4)) := ( t(\u03b4)[u\u2212 \u03b4z], r(\u03b4)[v \u2212 \u03b4w]+ \u2212 s(\u03b4)[v \u2212 \u03b4w]\u2212 ) \u2208 M\u03bb\u00b5. Recall also that I\u03bb\u00b5 \u2208 C1(H,R), where H = H1 0 (\u2126)\u00d7H1 0 (\u2126). \u2212 s\u2032(0)v\u2212 \u2212 w\u2225 as \u03b4 \u2192 0+.", "mime": "application/pdf"}, {"id": "ejde-682", "words": "7741", "extension": ".pdf", "flesch": "74", "author": "Hua, Yang; Lin, Xiaojie; Liu, Jiang; Lu, Haixia", "title": "Dynamics of traveling waves for predator-prey systems with Allee effect and time delay", "date": "2024", "keywords": "+ \u221e; delay; system", "summary": "Comparing the coefficients of \u03b5 and \u03b52, one has f1 = 0, f2 = 2UV \u03b1+ U + \u03b2V \u2212 2(\u03c3U \u2212 \u03c3U2 \u2212 \u03b7)U, h1 = 0, h2 = cX \u2212 (\u03c3U \u2212 \u03c3U2 \u2212 \u03b7)U + UV \u03b1+ U + \u03b2V , g1 = X, g2 = 0, r1 = 0, r2 = 0. Furthermore, under certain conditions, see [7] for more details, the system (2.3) admits the fourth equilibrium P\u2217(u\u2217, v\u2217, 0, 0), where u\u2217 is a positive root of the cubic equation \u03c3\u03b3\u03b2u3 \u2212 \u03c3\u03b3\u03b2u2 + (\u03b3\u03b2\u03b7 + \u03b3 \u2212 1)u\u2212 \u03b1 = 0, (2.4) and v\u2217 = \u03b3u\u2217 \u2212 u\u2217 \u2212 \u03b1 \u03b2 > 0.", "mime": "application/pdf"}, {"id": "ejde-683", "words": "7525", "extension": ".pdf", "flesch": "83", "author": "Sousa, Jose Vanterler da C.; Pigossi, Mariane; Nyamoradi, Nemat", "title": "Existence and multiplicity of solutions for fractional differential equations with p-Laplacian at resonance", "date": "2024", "keywords": "fractional", "summary": "4 J. V. D. C. SOUSA, M. PIGOSSI, N. NYAMORADI EJDE-2024/34 For the first eigenfunctions \u03c61(a) > 0, if we let V = span{\u03c61(a)}, then V \u22a5 = { \u03be \u2208 H\u03b1,\u03b2,\u03c8p : \u222b T 0 (\u03c6(a))p\u22121\u03bedx = 0 } . such that\u222b T 0 (\u2223\u2223\u2223HD\u03b1,\u03b2,\u03c8 0+ \u03be(x) \u2223\u2223\u2223p \u2212 a(x)|\u03be|p ) dx \u2a7e \u03bb(a) \u222b T 0 |\u03be|pdx (1.10) for any \u03be \u2208 V \u22a5. Similarly, we can define \u03bb1(b), \u03c61(b) and \u03bb(b).", "mime": "application/pdf"}, {"id": "ejde-685", "words": "11419", "extension": ".pdf", "flesch": "84", "author": "Hoang, Luan", "title": "Behavior near the extinction time for systems of differential equations with sublinear dissipation terms", "date": "2025", "keywords": "equation; extinction; function; o((t\u2217; t)1; theorem; time; tmax; y(t", "summary": "This expression and properties (5.15), (5.18) imply, as t \u2192 T\u2212 \u2217 , |y(t)\u2212 (T\u2217 \u2212 t)1/\u03b1\u03be\u2217| = O ( (T\u2217 \u2212 t)1/\u03b1(|eh1(t) (6.24) Utilizing this estimate in (6.23) gives |R\u03bbj v(t)|2 16 L. HOANG EJDE-2025/08 \u2264 e\u2212\u03b8\u00b5 \u222b t t\u0304 (T\u2217\u2212\u03c4)\u22121d\u03c4 |R\u03bbjv(t\u0304)|2 + C6 \u222b t t\u0304 e\u2212\u03b8\u00b5 \u222b t \u03c4 (T\u2217\u2212s)\u22121ds(T\u2217 \u2212 \u03c4)\u22121+2\u03b4/\u03b1d\u03c4 = (T\u2217 \u2212 t)\u03b8\u00b5 (T\u2217 \u2212 t\u0304)\u03b8\u00b5 |R\u03bbjv(t\u0304)|2 + C6(T\u2217 \u2212 t)\u03b8\u00b5 \u222b t t\u0304 (T\u2217 \u2212 \u03c4)\u22121+2\u03b4/\u03b1\u2212\u03b8\u00b5d\u03c4 = (T\u2217 \u2212 t)\u03b8\u00b5 (T\u2217 \u2212 t\u0304)\u03b8\u00b5 |R\u03bbj v(t\u0304)|2 + C6(T\u2217 \u2212 t)\u03b8\u00b5 2\u03b4/\u03b1\u2212 \u03b8\u00b5 ( (T\u2217 \u2212 t\u0304)2\u03b4/\u03b1\u2212\u03b8\u00b5 \u2212 (T\u2217 \u2212 t)2\u03b4/\u03b1\u2212\u03b8\u00b5 ) .", "mime": "application/pdf"}, {"id": "ejde-686", "words": "9801", "extension": ".pdf", "flesch": "83", "author": "Ngai , Sze-Man; Zhang, Meng-Ke; Zhao, Wen-Quan", "title": "Nodal sets and continuity of eigenfunctions of Krein-Feller operators", "date": "2025", "keywords": "eigenfunctions; function; g(x; nodal; theorem", "summary": "Hence the Green function G(x,y) is symmetric on \u2126 \u00d7 \u2126 i.e., there exists x0 \u2208 \u2126 such that u1(x0) = 0.", "mime": "application/pdf"}, {"id": "ejde-69", "words": "5887", "extension": ".pdf", "flesch": "88", "author": "Yu, Xiaozhu; ing, Shiwen; Lian, Hairong", "title": "Positive solutions for a class of phi-Laplacian differential systems with multiple parameters", "date": "2022", "keywords": "solution", "summary": "We prove the existence of positive solutions under the \u03c6-super-linear condition by means of the Guo-Krasnosel\u2019skii fixed point theorem and the topological degree. There are lots of im- portant results on positive solutions of nonlinear problems.", "mime": "application/pdf"}, {"id": "ejde-696", "words": "7213", "extension": ".pdf", "flesch": "75", "author": "Gnanasekaran, Shanmugasundaram; Nithyadevi, Nagarajan", "title": "Existence of global weak solution to tumor chemotaxis competition systems with loop and signal dependent sensitivity", "date": "2024", "keywords": "system; u1\u03f5; \u03b41 \u222b; \u03c9 u2; \u222b t; \u222b \u03c9", "summary": "\u2032 \u2264 3 4 \u222b T 0 \u222b \u2126 \u2223\u2223\u2207u1\u03f5 \u2223\u22234/3 + d41|\u2126|T 4 + M1 2 \u222b T 0 \u222b \u2126 u2 1\u03f5 + M1 2 \u222b T 0 \u222b \u2126 |\u2207v1\u03f5|2 + M2 2 \u222b T 0 \u222b \u2126 u2 1\u03f5 + M2 2 \u222b T 0 \u222b \u2126 |\u2207v2\u03f5|2 + \u03b41 \u222b T 0 \u222b \u2126 u1\u03f5 + \u03b41 \u222b T 0 \u222b \u2126 u2 1\u03f5 + \u03b41a1 2 \u222b T 0 \u222b \u2126 u2 1\u03f5 + \u03b41a1 2 \u222b T 0 \u222b \u2126 u2 2\u03f5 + \u03f5 \u222b T 0 \u222b \u2126 uq 1\u03f5 \u2264 C(T + 1). if u1 \u2208 L2 loc ( (0,\u221e);L2(\u2126) ) , u2 \u2208 L2 loc ( (0,\u221e);L2(\u2126) ) , v1 \u2208 L2 loc ( (0,\u221e);W 1,2(\u2126) ) , v1 \u2208 L2 loc ( (0,\u221e);W 1,2(\u2126) ) EJDE-2024/56 WEAK SOLUTION TO A TUMOR CHEMOTAXIS COMPETITION SYSTEM 5 and satisfies \u2212 \u222b \u221e 0 \u222b \u2126 u1\u03d5t = d1 \u222b \u2126 u10\u03d50 \u2212 \u222b \u221e 0 \u222b \u2126 \u2207u1 \u00b7 \u2207\u03d5+ \u222b \u221e 0 \u222b \u2126 \u03c71(v1)u1\u2207v1\u2207\u03d5 + \u222b \u221e 0 \u222b \u2126 \u03c72(v2)u1\u2207v2\u2207\u03d5+ \u03b41 \u222b \u221e 0 \u222b \u2126 u1(1\u2212 u1 \u2212 a1u2)\u03d5, \u2212 \u222b \u221e 0 \u222b \u2126 u2\u03d5t = d2 \u222b \u2126 u20\u03d50 \u2212 \u222b \u221e 0 \u222b \u2126 \u2207u2 \u00b7 \u2207\u03d5+ \u222b \u221e 0 \u222b \u2126 \u03be1(v1)u2\u2207v1\u2207\u03d5 + \u222b \u221e 0 \u222b \u2126 \u03be2(v2)u2\u2207v2\u2207\u03d5+ \u03b42 \u222b \u221e 0 \u222b \u2126 u2(1\u2212 u2 \u2212 a2u1)\u03d5, \u2212 \u222b \u221e 0 \u222b \u2126 v1\u03d5t = d3 \u222b \u2126 v10\u03d50 \u2212 \u222b \u221e 0 \u222b \u2126 \u2207v1 \u00b7 \u2207\u03d5+ \u03b11 \u222b \u221e 0 \u222b \u2126 u1\u03d5+ \u03b21 \u222b \u221e 0 \u222b \u2126 u2\u03d5 \u2212 \u03b31 \u222b \u221e 0 \u222b \u2126 v1\u03d5, \u2212 \u222b \u221e 0 \u222b \u2126 v2\u03d5t = d4 \u222b \u2126 v20\u03d50 \u2212 \u222b \u221e 0 \u222b \u2126 \u2207v2 \u00b7 \u2207\u03d5+ \u03b12 \u222b \u221e 0 \u222b \u2126 u1\u03d5+ \u03b22 \u222b \u221e 0 \u222b \u2126 u2\u03d5 \u2212 \u03b32 \u222b \u221e 0 \u222b \u2126 v2\u03d5, for all \u03d5 \u2208 C\u221e 0 (\u2126\u00d7 [0,\u221e)).", "mime": "application/pdf"}, {"id": "ejde-698", "words": "6118", "extension": ".pdf", "flesch": "83", "author": "Ding, Xin; Zheng, Xiu Min Zheng", "title": "Forms of entire solutions of partial differential difference equations with constant coefficients", "date": "2024", "keywords": "equation; f(z1; solutions; \u2202z1", "summary": "Some examples confirm the existence and the forms of transcendental entire solutions with finite order of such equations. Introduction In this article, we consider transcendental entire solutions of certain quadratic trinomial partial differential difference equations (PDDEs) in C2, related to the Fermat type functional equations with constant coefficients.", "mime": "application/pdf"}, {"id": "ejde-7", "words": "6373", "extension": ".pdf", "flesch": "71", "author": "D\u00edaz Palencia, Jos\u00e9 Luis", "title": "Semigroup theory and asymptotic profiles of solutions for a higher-order Fisher-KPP problem in R^N", "date": "2023", "keywords": "equation; fisher; function; operator; order; solutions", "summary": "\u2212 S(t)v\u20162 \u2264 \u2016S(t)\u20162 \u2016S(\u03c4)v \u2212 v\u20162 \u2264 mewt\u2016S(\u03c4)v \u2212 v\u20162. \u2212 v1)\u2212 v2(g \u2212 v2)]|2 } d\u03be = \u222b \u0393r \u03a5(\u03be) { |(v1 \u2212 v2)(g \u2212 (v1 \u2212 v2))|2 + 4\u2211 k=1 k\u2211 i=1 \u2223\u2223(k", "mime": "application/pdf"}, {"id": "ejde-70", "words": "10464", "extension": ".pdf", "flesch": "86", "author": "Guesmia, Aissa", "title": "Decay rates for two Cauchy thermoelastic laminated Timoshenko problems of type III with interfacial sli", "date": "2022", "keywords": "2\u03b50; case; equations; multiplying; timoshenko", "summary": "\u2212 \u03b5)|z\u0302|2 + (k3\u03bb3 \u2212 \u03b5)|\u03c6\u0302|2 + (\u03bb2 \u2212 \u03b5)|u\u0302|2 + (\u03bb4 \u2212 \u03bb3 \u2212 \u03b5)|\u03b8\u0302|2) \u2212 \u03be2((k1\u03bb5 \u2212 k1\u03bb4 \u2212 k1\u03bb2 \u2212 \u03b5)|v\u0302|2 + ( |\u03b3|\u03bb0 \u2212 \u03bb1 \u2212 \u03bb5 \u2212 \u03b5 ) |y\u0302|2 + (k4 \u2212 \u03b5)|\u03c3\u0302|2) + C\u03b5,\u03bb0,...,\u03bb9 f\u0303(\u03be)|\u03b7\u0302|2. (5.26) \u2212 \u03bb4 \u2212 \u03bb6 \u2212 \u03bb7.", "mime": "application/pdf"}, {"id": "ejde-700", "words": "11675", "extension": ".pdf", "flesch": "83", "author": "Mennuni, Federica; Salvatore, Addolorata", "title": "Radial bounded solutions for modified Schrodinger equations", "date": "2024", "keywords": "a(x; a.e; g(x", "summary": "[a(x, un,\u2207un) \u00b7 \u2207un +At(x, un,\u2207un)un] dx + \u222b B+ k,n k un a(x, un,\u2207un) \u00b7 \u2207un dx+ \u222b B+ k,n |un|p\u22122un(un \u2212 k) dx \u2212 \u222b B+ k,n g(x, un)R + k un dx \u2265 \u03b11 \u222b B+ k,n a(x, un,\u2207un) \u00b7 \u2207un dx\u2212 \u222b B+ k,n g(x, un)R + k un dx. Hence, from the previous inequalities, (A5) and (A6) it follows that \u03b10\u03b11 \u03b70 \u222b B+ k,n |\u2207un|p dx \u2264 \u27e8dJ (un), R + k un\u27e9+ \u222b B+ k,n g(x, un)R + k un dx.", "mime": "application/pdf"}, {"id": "ejde-703", "words": "12270", "extension": ".pdf", "flesch": "86", "author": "Cho, Namkyeong", "title": "Global gradient estimates \u00a0for \u00a0shear thinning-type Stokes system on the non-smooth domains", "date": "2024", "keywords": "c \u222b; dx+ c; ejde-2024/47; equations; lemma; shear; solution; \u03b5 \u222b; \u03c6(|\u2207w|; \u222b \u2212\u03c98", "summary": "dx \u2264 \u03b4, (1.8) where \u03b4 is the same as the one chosen in (i). Then,\u222b B+ 8 \u03c6(\u03b7|d+Dw|) dx \u2264 c \u222b B+ 8 \u03b72|d+V (Dw)|2 dx+ c \u222b B+ 8 \u03c6(|\u2207w|) dx, (3.5)\u222b B+ 8 |\u03c0w|2 dx \u2264 c \u222b B+ 8 \u03c6(|\u2207w|) \u03c6\u2217(1) + 1 dx. (3.6) 12 N. CHO EJDE-2024/47 Proof.", "mime": "application/pdf"}, {"id": "ejde-71", "words": "6422", "extension": ".pdf", "flesch": "92", "author": "Kurima , Shunsuke", "title": "Existence for a nonlocal Penrose-Fife type phase field system with inertial term", "date": "2023", "keywords": "l2(\u03c9; lemma", "summary": "Therefore, since vh \u2212 v\u03c4 = vh \u2212 v\u0302h + v\u0302\u03c4 \u2212 v\u03c4 + v\u0302h \u2212 v\u0302\u03c4 , we can prove Lemma 5.1 by (5.3)-(5.7), the Schwarz inequality, the Young inequality, (2.11), (2.13), Lemmas 4.1, 4.3, 4.8. \u2212 1 2 \u2016\u03b8n\u20162L2(\u2126) + 1 2 \u2016\u03b8n+1 \u2212 \u03b8n\u20162L2(\u2126) + h(\u2212\u2206un+1, \u03b8n+1)L2(\u2126) = h(fn+1, \u03b8n+1)L2(\u2126) \u2212 h(vn+1, \u03b8n+1)L2(\u2126). (4.11) Here, since un+1 = \u2212 1 \u03b8n+1 , \u03b8n+1 > 0, and gn+1 \u2264 0, we have that h(\u2212\u2206un+1, \u03b8n+1)L2(\u2126) = h \u222b \u2126 \u2207un+1 \u00b7 \u2207\u03b8n+1 + h \u222b \u2202\u2126 un+1\u03b8n+1 \u2212 h \u222b \u2202\u2126 gn+1\u03b8n+1 \u2265 h \u222b \u2126 |\u2207 ln \u03b8n+1|2 \u2212 h|\u2202\u2126|.", "mime": "application/pdf"}, {"id": "ejde-718", "words": "7258", "extension": ".pdf", "flesch": "77", "author": "Doresic, Tvrtko; Pazanin, Igor", "title": "Curved-pipe flow with boundary conditions involving Bernoulli pressure", "date": "2024", "keywords": "cos\u03b1; pipe; sin\u03b1; \u03b5 \u03ba; \u2202y2; \u2202y3", "summary": "\u2212 V 1 0 \u2202V 1 0 \u2202y2 = 0 in \u2126 , \u2212\u03bd\u2206y\u2217V 3 1 + \u2202P2 \u2202y3 \u2212 V 1 0 \u2202V 1 0 \u2202y3 = 0 in \u2126 , \u2202V 2 1 \u2202y2 + \u2202V 3 1 \u2202y3 = 0 in \u2126, V 2 1 = V 3 1 = 0 on \u0393 . y\u2217)V 1 0 \u2202V 1 0 \u2202y3 \u2212 V 1 1 \u2202V 1 0 \u2202y3 \u2212 V 1 0 \u2202V 1 1 \u2202y3 = 0 in \u2126 , which, since V 2 1 = V 3 1 = 0 and V 1 0 = V 1 0 (y\u2217), reduces to the problem \u2212 \u03bd ( \u2206y\u2217V 2 2 + \u03ba\u2032V 1 0 cos\u03b1+ \u03ba\u03c4V 1 0 sin\u03b1 ) + \u2202P3 \u2202y2 \u2212 \u03ba(e\u03b1 \u00b7 y\u2217)V 1 0 \u2202V 1 0 \u2202y2 \u2212 V 1 1 \u2202V 1 0 \u2202y2 \u2212 V 1 0 \u2202V 1 1 \u2202y2 = 0 in \u2126 , \u2212 \u03bd ( \u2206y\u2217V 3 2 \u2212 \u03ba\u2032V 1 0 sin\u03b1+ \u03ba\u03c4V 1 0 cos\u03b1 ) + \u2202P3 \u2202y3 \u2212 \u03ba(e\u03b1 \u00b7 y\u2217)V 1 0 \u2202V 1 0 \u2202y3 \u2212 V 1 1 \u2202V 1 0 \u2202y3 \u2212 V 1 0 \u2202V 1 1 \u2202y3 = 0 in \u2126 , \u2202V 1 1 \u2202x1 + ( \u03ba\u2032 (e\u03b1 \u00b7 y\u2217) + \u03ba\u03c4 ( e\u22a5\u03b1 \u00b7 y\u2217 ))", "mime": "application/pdf"}, {"id": "ejde-719", "words": "2462", "extension": ".pdf", "flesch": "77", "author": "Gil, Michael", "title": "Delay-dependent stability conditions for delay differential equations\u00a0with unbounded operators in Banach spaces", "date": "2024", "keywords": "differential; stability", "summary": "= \u03d5(t) (\u2212h \u2264 t \u2264 0), (1.2) where \u03d5 \u2208W ([\u2212h, 0],X ) \u2229D(A) is given. + \u222b t 0 eA(t\u2212s)By(s\u2212 h)ds.", "mime": "application/pdf"}, {"id": "ejde-72", "words": "10490", "extension": ".pdf", "flesch": "86", "author": "Ye, Qin; Zhang, Yinghui", "title": "Space-time decay rates of a two-phase flow model with magnetic field in R^3", "date": "2023", "keywords": "decay; inequality; lemma; space; v)\u20162l2 \u03b3; \u03b3\u22121", "summary": "Let (\u03c1\u2212 \u03c1\u0304, u, n\u2212 n\u0304, v, B) be the strong solution to the system (1.1)- (1.2) with initial data (\u03c10 \u2212 \u03c1\u0304, u0, n0 \u2212 n\u0304, v0, B0) belonging to the Schwartz class S. Under the assumptions in Theorem 1.1, then there exists a large enough T such that \u2016\u2207k(u\u2212 v)(t)\u2016L2 \u03b3 \u2264 C(1 + t)\u2212 5 4\u2212 k 2+\u03b3 , (1.15) EJDE-2023/41 SPACE-TIME DECAY RATES 7 for all t > T , 0 \u2264 k \u2264 `\u2212 2 and \u03b3 \u2265 0, where C is a positive constant independent of t. Now, let us outline the strategies for proving Theorem 1.1 and 1.4, and explain the main difficulties in the process. \u03b3\u22121 \u03b3 , (1.16) for t is large enough and \u03b3 > 3 2 , where E(t) := \u2016(m,u, \u03c3, v,B)\u20162L2 \u03b3 and C0, C1, C2 are positive constants independent of t. Applying Lemma 2.5 for (1.16) and the interpolation trick, we show that the Theorem 1.1 holds for case k = 0.", "mime": "application/pdf"}, {"id": "ejde-720", "words": "8678", "extension": ".pdf", "flesch": "84", "author": "Karakostas, George L.", "title": "Solving linear differential equations with mixed arguments", "date": "2024", "keywords": "differential; equation; interval; m=0; solution", "summary": "Differential equations with mixed arguments; nonsingular matrices. 1 2 G. L. KARAKOSTAS EJDE-2024/54 In this article we present a type of differential equations and give some answers to these questions.", "mime": "application/pdf"}, {"id": "ejde-73", "words": "9623", "extension": ".pdf", "flesch": "80", "author": "Li, Cuicui; Liu, Fang", "title": "Viscosity solutions to the infinity Laplacian equation with lower terms", "date": "2023", "keywords": "c(\u03c9; existence; f(x; infinity; problem; solution; viscosity", "summary": "Then there exist x0 \u2208 \u2126 and \u03d5 \u2208 C2(\u2126) such that \u03d5(x0) = u(x0), u(x)\u2212 \u03d5(x) \u2265 0, x \u2208 B\u03c1(x0) \u2286 \u2126, for some \u03c1 > 0, but \u2206h \u221e\u03d5(x0) > f(x0, u(x0)). We establish the existence and uniqueness of viscosity solutions to the Dirichlet problem \u2206h \u221eu = f(x, u), in \u2126, u = q, on \u2202\u2126, where q \u2208 C(\u2202\u2126), h > 1, \u2206h \u221eu = |Du|h\u22123\u2206\u221eu.", "mime": "application/pdf"}, {"id": "ejde-734", "words": "10842", "extension": ".pdf", "flesch": "77", "author": "Karuppusamy, Yadhavan; Lingeshwaran, Shangerganesh; Jeyaraj, Manimaran", "title": "Solvability of an attraction-repulsion chemotaxis Navier-Stokes system with arbitrary porous medium diffusion", "date": "2024", "keywords": "+ 2\u03b1; chemotaxis; existence; p+\u03b1; solutions; system; \u222522; \u222b r3", "summary": "\u2225u\u22251+\u03b1 1+\u03b1 + \u2225\u2207v\u222522 + \u2225\u2207w\u222522 + \u2225z\u222522 ) + \u222b T 0 ( \u2225\u2207u 1+\u03b1 2 \u222522 + \u2225\u2207u 1+2\u03b1 2 \u222522 + \u2225\u2206v\u222522 + \u2225\u2206w\u222522 + \u2225\u2207z\u222522 ) and either one of the assumptions (2.5) or (2.59) holds by replacing R3 by \u2126. Then for each T > 0, system (2.2) with boundary conditions (2.74) possesses a weak soluion (u, v, w, z) that satisfies sup 0\u2264t\u2264T (\u222b \u2126 u| log u| dx+ \u2225u\u22251+\u03b1 1+\u03b1 + \u2225\u2207v\u222522 + \u2225\u2207w\u222522 + \u2225z\u222522 ) + \u222b T 0 ( \u2225\u2207u 1+\u03b1 2 \u222522 + \u2225\u2207u 1+2\u03b1 2 \u222522 + \u2225\u2206v\u222522 + \u2225\u2206w\u222522 + \u2225\u2207z\u222522 )", "mime": "application/pdf"}, {"id": "ejde-741", "words": "9251", "extension": ".pdf", "flesch": "74", "author": "de Carvalho, Pit\u00e1goras; Demarque, Reginaldo; L\u00edmaco, Juan; Viana, Luiz", "title": "Null-controllability for 1-D degenerate quasilinear parabolic equations", "date": "2025", "keywords": "controllability; equations; l2(q", "summary": "Moreover, if u0 \u2208 H1 a , then u \u2208 U := H1(0, T ;L2(0, 1)) \u2229 L2(0, T ;H2 a) \u2229 C0([0, T ];H1 a), and there exists a constant CT > 0 such that sup t\u2208[0,T ] (\u2225u(t)\u22252H1 a ) + \u222b T 0 ( \u2225ut|2L2(0,1) + \u2225(aux)x\u22252L2(0,1) ) \u2264 CT ( \u2225u0\u22252H1 a + \u2225g\u22252L2(Q) + \u2225h\u22252L2(Q\u03c9) ) . \u2225\u03b4, that is, \u2225f\u2225\u03b4 = (\u222b T 0 \u222b 1 0 \u03b4f2 dx dt )1/2 for each f \u2208 L2(Q; \u03b4).", "mime": "application/pdf"}, {"id": "ejde-745", "words": "4217", "extension": ".pdf", "flesch": "75", "author": "Sikorska-Nowak, Aneta", "title": "Existence of pseudosolutions for dynamic fractional differential equations", "date": "2024", "keywords": "fractional", "summary": "In this article, we consider the existence of pseudosolutions for boundary value problem for fractional differential equations of the form C T \u2206\u03b1x(t) = f(t, x(t)), for t \u2208 Ia = [0, a] \u2229 T, x(0) = x0, x0 \u2208 E, where C T \u2206\u03b1x(t), \u03b1 \u2208 (0, 1] denotes the Caputo fractional derivative, T denotes a time scale, and the function f is weakly-weakly sequentially continuous with values in a Banach space E and satisfies some boundary conditions and con- ditions expressed in terms of measures of weak non-compactness. In this paper, we consider the existence of a pseudosolution for the boundary value problem for fractional differential equations of the form C T\u2206 \u03b1x(t) = f(t, x(t)), for t \u2208 Ia = [0, a] \u2229 T, x(0) = x0, x0 \u2208 E, (1.1) where C T\u2206 \u03b1x(t), \u03b1 \u2208 (0, 1] is the Caputo fractional derivative, T denotes a time scale.", "mime": "application/pdf"}, {"id": "ejde-747", "words": "4532", "extension": ".pdf", "flesch": "80", "author": "Zheng, Lan-Ling; Ding, Hui-Sheng", "title": "Massera type theorems for abstract non-autonomous evolution equations", "date": "2024", "keywords": "lim; periodic", "summary": "As appli- cation, we present an existence result on periodic mild solutions to abstract nonautonomous semilinear evolution equations. As application of our Massera type theorems, in the last part of this paper, we establish an existence result on periodic mild solutions to (1.2).", "mime": "application/pdf"}, {"id": "ejde-75", "words": "8547", "extension": ".pdf", "flesch": "87", "author": "Xu, Hong Yan; Haldar, Goutam", "title": "Solutions of complex nonlinear functional equations including second order partial differential and difference in C^2", "date": "2023", "keywords": "equations; f(z1; order; solutions; view", "summary": "In view of the fact that a1c1 + a2c2 = 4k\u03c0i, k \u2208 Z, it follows from the second equation of (3.23) that\u222b z1 0 [G0(z2 \u2212 \u03b2z1 + c2 \u2212 \u03b2c1)\u2212G0(z2 \u2212 \u03b2z1)]dz1 +G1(z2 \u2212 \u03b1z1 + c2 \u2212 \u03b1c1)\u2212G1(z2 \u2212 \u03b1z1) = 0. Let \u03b4 = \u03b7 = 4, \u03be = 5, c1 = 2, c2 = 3, a0 = 1, L(z) = z1 \u2212 z2 and g(z1, z2)", "mime": "application/pdf"}, {"id": "ejde-754", "words": "6169", "extension": ".pdf", "flesch": "86", "author": "Banerjee, Abhijit; Sarkar, Jhuma", "title": "Existence and forms of entire solutions to system \u00a0of non-linear partial differential equations", "date": "2024", "keywords": "s(r; solution", "summary": "Let b10 = 1, b01 = 1, b11 = 1, b20 = 1, b02 = 1, d1 = 1, d2 = \u22121, c1 = c2 = 1, W1 = \u03c0i 4 , W2 = \u03c0i 4 . The main objective of this article is to explore the existence and forms of transcendental entire solutions of some systems of non-linear partial differential equations.", "mime": "application/pdf"}, {"id": "ejde-756", "words": "5019", "extension": ".pdf", "flesch": "78", "author": "Jia, Yan-Na; Jin, Can; Yu, Xiu-Fang", "title": "Output tracking for a 1-D wave equations with spatially varying coefficients and subject to unknown disturbances", "date": "2024", "keywords": "control; equation; error; output; system; tracking; wave", "summary": "= \u2212ma(1)y\u03032t (1, t)\u2212 ka(0)y\u03032t (0, t). Solving (2.34) gives \u03a6\u0302(t) = e\u03a5t\u03a6\u0302(0) + \u222b t 0 e\u03a5(t\u2212\u03c4)K\u0302\u03c7(\u03c4)d\u03c4.", "mime": "application/pdf"}, {"id": "ejde-759", "words": "3921", "extension": ".pdf", "flesch": "74", "author": "Banagere Erajikkappa, Manjunath; Waghamore, Harina P.", "title": "Entire solutions for non-linear differential-difference equations", "date": "2025", "keywords": "differential; equations; solutions", "summary": "Preliminaries To prove our results, we first give some Lemmas as follows: The first Lemma presents the difference analogs of the Logarithmic Derivative Lemma, a crucial tool in investigating complex difference equations. [2] Chen, M. F.; Cui, N.; On zeros and growth of solutions of complex difference equations, Adv. Difference Equ., 2021 (2021), 16.", "mime": "application/pdf"}, {"id": "ejde-76", "words": "4413", "extension": ".pdf", "flesch": "77", "author": "Hu, Rong; Sofonea, Mircea", "title": "Duality arguments for well-posedness of history-dependent variational inequalities", "date": "2022", "keywords": "c([0; problem", "summary": "Problem P. Find a function u \u2208 C([0, T ];V ) such that the following inequality holds: u(t) \u2208 K(t) and (Au(t), v \u2212 u(t))V + (Su(t), v \u2212 u(t))V \u2265 (f(t), v \u2212 u(t))V (3.1) for all v \u2208 K(t) and t \u2208 Under assumptions (H2)\u2013(H4), the operator D : C([0, T ];V )\u2192 C([0, T ];V ) defined by Du(t) = Au(t) + Su(t)\u2212 f(t) \u2200u \u2208 C([0, T ];V ), t \u2208", "mime": "application/pdf"}, {"id": "ejde-761", "words": "8596", "extension": ".pdf", "flesch": "66", "author": "Diaz Palencia, Jose Luis", "title": "Instability of energy solutions, travelling waves, and scaling invariance for a fourth-order p-Laplacian operator with superlinear reaction", "date": "2024", "keywords": "diffusion; energy; equation; lemma; operator; order; problem; solution", "summary": "Solution profiles for low values of TW-speed. The analysis of problem (1.1) begins with the definition of energy solutions, as proposed for general diffusion in [26].", "mime": "application/pdf"}, {"id": "ejde-77", "words": "5211", "extension": ".pdf", "flesch": "82", "author": "Penney, Richard C.; Urban, Roman", "title": "Poisson measures on semi-direct products of infinite-dimensional Hilbert spaces", "date": "2022", "keywords": "measure; poisson", "summary": "Then from (4.1) for 0 < s < t,\u222b t 0 EaL\u03c3t\u2212s\u03b2 v(s, x, \u03c3t\u2212s) = Ea \u222b t 0 L\u03c3t\u2212s\u03b2 U\u03c3(0, s)f(x, \u03c3t\u2212s) = \u222b t 0 Ea \u222b `2 \u221e\u2211 j=1 e2\u03bbj(\u03c3t\u2212s)\u03b2j\u2202 2 xjv(x+ y)N2[\u03b2]A\u03c3(s,0)(dy) ds. Since \u2223\u2223Ea \u222b t 0 e2\u03bbj(\u03c3t\u2212s) ds \u2223\u2223 = \u2223\u2223Ea \u222b t 0 e2\u03bbj(\u03c3u) du \u2223\u2223 = \u2223\u2223Ea \u222b t 0 e2(\u03c3u)j du \u2223\u2223 = \u2223\u2223Ea \u222b t 0 e2(bu)j\u2212\u03b1jt du \u2223\u2223 \u2264 \u2223\u2223\u2223\u2223Ea \u222b t 0 e2(bu)j du \u2223\u2223\u2223\u2223 = Ct we obtain (since \u03b2 \u2208 `1) that |La\u03b2v(s, x, a)| \u2264 \u2223\u2223\u2223\u2016v\u20162\u221e \u221e\u2211 j=1 \u03b2jEa \u222b t 0 e2\u03bbj(\u03c3t\u2212s) ds \u2223\u2223\u2223 \u2264 \u2016v\u20162\u221eCt \u2223\u2223 \u221e\u2211 j=1 \u03b2j \u2223\u2223 \u2264 Ct\u2016v\u2016\u221e\u2016\u03b2\u2016`1 .", "mime": "application/pdf"}, {"id": "ejde-771", "words": "7154", "extension": ".pdf", "flesch": "75", "author": "Zhang, Xuping; Ding, Kaibo; Chen, Pengyu", "title": "Existence of positive S-asymptotically omega-periodic solutions of time-space fractional \u00a0nonlocal reaction-diffusion equations", "date": "2025", "keywords": "fractional; k=1", "summary": "[29] X. Shu, F. Xu, Y. Shi; S-asymptotically \u03c9-positive periodic solutions for a class of neutral fractional differential equations. Tk 0 (Tk \u2212 s)\u03b1\u22121K\u03b1,\u03b2(Tk \u2212 s)G(s, u(s))ds + \u222b t 0 (t\u2212 s)\u03b1\u22121K\u03b1,\u03b2(t\u2212 s)G(s, u(s))ds. (3.2) Moreover, if u(t) \u2265 \u03b8 for all t \u2265 0, then it is said to be a positive mild solution of nonlocal problem (3.1).", "mime": "application/pdf"}, {"id": "ejde-772", "words": "4414", "extension": ".pdf", "flesch": "75", "author": "Khaider, Hassan; Azanzal, Achraf ; Raji, Abderrahmane", "title": "Well-posedness of solutions for the 2D stochastic quasi-geostrophic equation in critical Fourier-Besov-Morrey spaces", "date": "2024", "keywords": "equations; sup; \u2225\u03c6j", "summary": "Consequently, stochastic partial differential equa- tions (SDE) such as quasi-geostrophic equations (QG), stochastic Navier-Stokes equations are gaining more and more interest in fluid mechanics research. To examine how stochastic forces affect quasi-geostrophic equations, we first present the outcome of the deterministic quasi-geostrophic equations, or the case g = 0 in (1.1).", "mime": "application/pdf"}, {"id": "ejde-774", "words": "8584", "extension": ".pdf", "flesch": "73", "author": "Garg, Swati; Sardar, Bidhan Chandra Sardar", "title": "Optimal control problem for Stokes systems: asymptotic analysis via unfolding method in a perforated domain", "date": "2023", "keywords": "boundary; control; domain; l2(o; problem; stokes", "summary": "[9] B. Cabarrubias; Homogenization of optimal control problems in perforated domains via pe- riodic unfolding method, Appl. MR 2563641 [26] I. Mishra; Homogenization of boundary optimal control problem, Electron.", "mime": "application/pdf"}, {"id": "ejde-778", "words": "10341", "extension": ".pdf", "flesch": "76", "author": "Liu, Mengqian; Niu, Lei; Wu, Zhigang", "title": "Existence and uniqueness of global strong solutions for 3D fractional compressible systems", "date": "2025", "keywords": "3\u2211 i=1; ejde-2025/35; equations; h\u0307s\u22121; i=1; lemma; navier; solution; stokes; \u2212 \u00b5)\u03bb2\u03b1u; \u27e8[\u2206j", "summary": "Specifically, |I22| = | \u2212 3\u2211 i=1 \u27e8[\u2206j , \u00b5\u2032 (\u03ba+ 1 a\u03c1) a \u2212 \u00b5]Di\u039b 2\u03b1u, Diuj\u27e9 | \u2272 3\u2211 i=1 cj2 \u2212js\u2225\u03c1\u2225Hs+1\u2225Di\u2207\u039b2\u03b1\u22122u\u2225Hs\u2225Diuj\u2225, |I23| = | \u2212 \u27e8[\u2206j ,u \u00b7 \u2207]\u2207\u03c1,\u2207\u039b2\u03c1j\u27e9| \u2272 cj2 \u2212js\u2225\u2207u\u2225Hs\u2225\u2207\u03c1\u2225Hs\u2225\u2207\u039b2\u03c1j\u2225, |I24| = | \u2212 \u27e8[\u2206j ,u \u00b7 \u2207]\u2207u,\u2207\u039b2uj\u27e9| \u2272 cj2 \u2212js\u2225\u2207u\u2225Hs\u2225\u2207u\u2225Hs\u2225\u2207\u039b2uj\u2225, |I25| = | \u2212 1 a \u27e8[\u2206j , \u03c1]\u2207divu,\u2207\u039b2\u03c1j\u27e9| \u2272 cj2 \u2212js\u2225\u2207\u03c1\u2225Hs\u2225 divu\u2225Hs\u2225\u2207\u039b2\u03c1j\u2225, |I26| = | \u2212 1 a \u27e8[\u2206j , \u03c1]\u22072\u03c1,\u2207\u039b2uj\u27e9| \u2272 cj2 \u2212js\u2225\u2207\u03c1\u2225Hs\u2225\u2207\u03c1\u2225Hs\u2225\u2207\u039b2uj\u2225, |I27| = |\u27e8[\u2206j , ( \u00b5\u2032 (\u03ba+ 1 a\u03c1) a \u2212 \u00b5)]\u2207\u039b2\u03b1u,\u2207\u039b2uj\u27e9| \u2272 cj2 \u2212js\u2225\u03c1\u2225Hs+1\u2225\u039b2\u03b1u\u2225Hs\u2225\u2207\u039b2uj\u2225. Inserting the above inequalities about I1 \u2212 I27 into (3.16), we have 1 2 d dt (\u2225\u03c1j\u22252 + \u2225uj\u22252 + 3\u2211 i=1 \u2225Di\u03c1j\u22252 + 3\u2211 i=1 \u2225Diuj\u22252 + \u2225\u039b2\u03c1j\u22252 + \u2225\u039b2uj\u22252 + 2\u03b21\u27e8\u2207\u03c1j ,uj\u27e9+ 2\u03b22 3\u2211 i=1 \u27e8Di\u2207\u03c1j , Diuj\u27e9) + \u27e8 \u00b5\u2032 (\u03ba+ 1 a\u03c1) a \u039b\u03b1uj ,\u039b \u03b1uj\u27e9 + 3\u2211 i=1 \u27e8 \u00b5\u2032 (\u03ba+ 1 a\u03c1) a Di\u039b \u03b1uj , Di\u039b \u03b1uj\u27e9 + \u27e8( \u00b5\u2032 (\u03ba+ 1 a\u03c1) a \u2212 \u00b5)\u2207\u039b1+\u03b1uj ,\u2207\u039b1+\u03b1uj\u27e9 + \u00b5\u2225\u039b2+\u03b1uj\u22252 + \u03b21\u03ba\u2225\u2207\u03c1j\u22252 + \u03b22\u03ba 3\u2211 i=1 \u2225Di\u2207\u03c1j\u22252 \u2272 \u03b21\u03ba\u2225divu\u22252 + \u03b22\u03ba 3\u2211 i=1 \u2225Di divu\u22252 + 8\u03f51\u2225\u2207\u03c1j\u22252 + 5\u03f51\u2225\u039b2\u03c1j\u22252 + 4\u03f51 3\u2211 i=1 \u2225Di\u2207\u03c1j\u22252 + 5\u03f51\u2225\u039b\u03b1uj\u22252 (3.17) + 4\u03f51 3\u2211 i=1 \u2225\u039b\u03b1Diuj\u22252 + 7\u03f51\u2225\u039b\u03b1\u039b2uj\u22252 + 2\u03f51 3\u2211 i=1 \u2225\u039b\u03b1 divDiuj\u22252 + \u03f51\u2225\u2207\u039b1+\u03b1uj\u22252 + C\u03f51\u03b2 2 1\u2225\u039b2\u03b1uj\u22252 + C\u03f51\u03b2 2 2 3\u2211 i=1 \u2225Di\u039b 2\u03b1uj\u22252 + 2\u22122jC\u03f51(\u2225\u2206j(u \u00b7 \u2207\u03c1)\u22252 + \u2225\u2206j(\u03c1divu)\u22252) + 2\u22122j\u03b1C\u03f51(\u2225\u2206j(u \u00b7 \u2207u)\u22252 + \u2225\u2206j(\u03c1\u2207\u03c1)\u22252) EJDE-2025/35 FRACTIONAL COMPRESSIBLE SYSTEMS 17 + C\u03f51 3\u2211 i=1 ( \u2225Di\u2206j(u \u00b7 \u2207\u03c1)\u22252 + \u2225Di\u2206j(\u03c1divu)\u22252 ) + 2\u22122j\u03b1C\u03f51 3\u2211 i=1 ( \u2225Di\u2206j(u \u00b7 \u2207u)\u22252 + \u2225Di\u2206j ( \u03c1\u2207\u03c1)\u22252 + \u2225\u2225\u2206j(Di( \u00b5\u2032 (\u03ba+ 1 a\u03c1) a \u2212 \u00b5)\u039b2\u03b1u) \u2225\u22252) + C\u03f51 ( \u2225 div\u2206j(\u2207u \u00b7 \u2207\u03c1)\u22252 + \u2225 div\u2206j(\u2207\u03c1divu)\u22252 ) + 2\u22122j\u03b1C\u03f51\u2225\u2207u\u22252L\u221e\u2225\u22072uj\u22252 + 2\u22122j\u03b1C\u03f51\u2225 div u\u22252L\u221e\u2225\u039b2uj\u22252 + 2\u22122j\u03b1C\u03f51\u2225div\u2206j(\u2207u \u00b7 \u2207u)\u22252 + 2\u22122j\u03b1C\u03f51\u2225div\u2206j(\u2207\u03c1\u2207\u03c1)\u22252 + C\u03f51\u2225\u2207u\u22252L\u221e\u2225\u22072\u03c1j\u22252 + C\u03f51\u2225 divu\u22252L\u221e\u2225\u039b2\u03c1j\u22252 + C\u03f51\u2225\u2207\u03c1\u22252L\u221e\u2225\u2207 divuj\u22252 + 2\u22122j\u03b1C\u03f51\u2225\u2207\u03c1\u22252L\u221e(\u2225\u22072\u03c1j\u22252 + \u2225\u039b2\u03c1j\u22252) + 2\u22122j\u03b1C\u03f51\u2225div\u2206j(\u2207( \u00b5\u2032 (\u03ba+ 1 a\u03c1) a \u2212 \u00b5)\u039b2\u03b1u)\u22252 + 2\u22122j\u03b1C\u03f51\u03b2 2 1(\u2225\u2207\u2206j(u \u00b7 \u2207\u03c1)\u22252 + \u2225\u2207\u2206j(\u03c1divu)\u22252) + C\u03f51\u03b2 2 1 ( \u2225\u2206j(\u03c1\u2207\u03c1)\u22252 + \u2225\u2206j(u \u00b7 Similarly, |I3| = | \u2212 3\u2211 i=1 \u27e8Di\u2206j(u \u00b7 \u2207\u03c1), Di\u03c1j\u27e9 \u2212 3\u2211 i=1 1 a \u27e8Di\u2206j(\u03c1divu), Di\u03c1j\u27e9| \u2272 C\u03f51 3\u2211 i=1 \u2225Di\u2206j(u \u00b7 \u2207\u03c1)\u22252 + C\u03f51 3\u2211 i=1 \u2225Di\u2206j(\u03c1 divu)\u22252 + 2\u03f51\u2225\u2207\u03c1j\u22252, 14 M. LIU, L. NIU, Z. WU EJDE-2025/35 |I4|", "mime": "application/pdf"}, {"id": "ejde-78", "words": "7207", "extension": ".pdf", "flesch": "86", "author": "Teles, Ricardo de Sa", "title": "Pullback attractors for non-autonomous Bresse systems", "date": "2022", "keywords": "+ \u03c8; \u2212 \u222b", "summary": "= \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0 \u03d5\u2032 \u03c8\u2032 w\u2032 k \u03c11 (\u03d5x + \u03c8 + lw)x + k0l \u03c11 (wx \u2212 l\u03d5) b \u03c12 \u03c8xx \u2212 k \u03c12 (\u03d5x + \u03c8 + lw) k0 \u03c11 (wx \u2212 l\u03d5)x \u2212 kl \u03c11 (\u03d5x + \u03c8 + lw) \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb , with domain D(B1) = (H2(0, L) \u2229 H1 0 (0, L))3 \u00d7 H1 0 (0, L)3, and B2 : H \u2192 H, is given by B2y (3.23) Now we estimate \u03a8\u2032(t), \u03a8\u2032(t) = \u03c11\u2016\u03d5t\u20162 + \u03c12\u2016\u03c8t\u20162 + \u03c11\u2016wt\u20162 \u2212 b\u2016\u03c8x\u20162 \u2212 k\u2016\u03d5x + \u03c8 + lw\u20162 \u2212 k0\u2016wx \u2212 l\u03d5\u20162 \u2212 \u222b", "mime": "application/pdf"}, {"id": "ejde-784", "words": "6644", "extension": ".pdf", "flesch": "78", "author": "Kryspin, Marek", "title": "Oseledets decomposition on sub semiflow", "date": "2024", "keywords": "decomposition; oseledets; \u03b8\u22121\u03c9", "summary": "For any family of subspaces {W (\u03c9)}\u03c9\u2208\u21260 of X1 such that the equality U (1) \u03c9 (t)W (\u03c9) = W (\u03b8t\u03c9) holds for all t \u2265 0 and all \u03c9 \u2208 \u21260, there exists a family of subspaces {V (\u03c9)}\u03c9\u2208\u21260 of X2 such (i) iV (\u03c9) = W (\u03c9) for any \u03c9 \u2208 \u21260, (ii) U (2) \u03c9 (t)V (\u03c9) = V (\u03b8t\u03c9) for all t \u2265 0 and \u03c9 \u2208 \u21260. U (1) \u03c9 (1) \u2223\u2223 E (1) j (\u03c9) \u25e6G(\u03c9)\u22121, \u03c9 \u2208 \u21260, generates a two-sided discrete-time linear skew-product dynamical system \u03a6\u0302 = ((U\u0302\u03c9(n)), (\u03b8n)) on \u21260 \u00d7 Rl, with U\u0302\u03c9(n) := G(\u03b8n\u03c9) \u25e6", "mime": "application/pdf"}, {"id": "ejde-786", "words": "5088", "extension": ".pdf", "flesch": "83", "author": "Dong, Sitong; Zhang, Xin; Jin, Yuanfeng", "title": "A second order convergent difference scheme for the initial-boundary value problem of Rosenau-Burgers equation", "date": "2024", "keywords": "scheme", "summary": "\u2212 1, 0 \u2264 k \u2264 N \u2212 1, (3.8) V k i = \u03b42xU k i +Qk i , 1 \u2264 i \u2264M \u2212 1, 0 \u2264 k \u2264 N, (3.9) there exist constants c1 and c2 such that |Rk+ 1 2 i | \u2264 c1(\u03c4 2 + h2), 1 \u2264 i \u2264M \u2212 1, 0 \u2264 k \u2264 N \u2212 1, |Qk i | \u2264 i \u2212 \u03c8(uk+ 1 2 , uk+ 1 2 )i] = R k+ 1 2 i , 1 \u2264 i \u2264M \u2212 1, 0 \u2264 k \u2264 N \u2212 1, (5.1) fki = \u03b42xe k i +Qk i , 1 \u2264 i \u2264M \u2212 1, 0 \u2264 k \u2264 N, (5.2) e0i = 0, 1 \u2264 i \u2264M \u2212 1, (5.3) ek0 = 0, ekM = 0, 0 \u2264 k \u2264 N, (5.4) fk0 = 0, fkM = 0, 0 \u2264 k \u2264 N. (5.5) It follows from (5.2) that f k+ 1 2 i = \u03b42xe k+ 1 2 i +Q k+ 1 2 i , 1 \u2264 i \u2264M \u2212 1, 0 \u2264 k \u2264 N \u2212 1.", "mime": "application/pdf"}, {"id": "ejde-788", "words": "11170", "extension": ".pdf", "flesch": "84", "author": "Polyakov, Dmitry M.", "title": "Asymptotic behavior of eigenvalues of fourth-order differential operators with spectral parameter in the boundary conditions", "date": "2024", "keywords": "+ o(n\u22122; asymptotics; behavior; det; differential; eigenvalues; equation; form; matrix; order", "summary": "Recall that z = \u03bb1/4, z \u2208 Z, \u03bb \u2208 C, where Z = { z \u2208 C : arg z \u2208 ( \u2212 \u03c0 4 , \u03c0 4 ]} , Z = { z \u2208 C : arg z \u2208 ( \u2212 \u03c0 4 , \u03c0 4 )} . \u00d7 ( 1 + (\u03b6\u03c3,14 \u2212 \u03b6\u03c3,24 \u2212 \u03b6\u03c3,34 + \u03b6\u03c3,44)(1, z) +O(z\u2212\u03c3\u22121) )", "mime": "application/pdf"}, {"id": "ejde-79", "words": "10132", "extension": ".pdf", "flesch": "75", "author": "Al Nazer, Safaa; Rosier, Carole; Tsegmid, Munkhgerel", "title": "Mathematical analysis of a Dupuit-Richards model", "date": "2022", "keywords": "equation; flow; hbot; model; problem; richards", "summary": "Dupuit approximation reads H\u0303 ' H|z=h\u2212 , the pressure P thus satisfies in \u2126\u2212t P (t, x, z) = \u03c10g ( H\u0303(t, x)\u2212 z ) for t \u2208 = {u(t, \u00b7) \u2208 H1(\u2126t), t \u2208", "mime": "application/pdf"}, {"id": "ejde-792", "words": "3754", "extension": ".pdf", "flesch": "77", "author": "Gao, Siyu; Liu, Qingbo; Sun, Yingxin", "title": "Local bifurcation structure and stability of the mean curvature equation in the static spacetime", "date": "2024", "keywords": "curvature; mean; \u03bb1 h0", "summary": "Bifurcation; mean curvature operator; stability. [6] C. Bereanu, P. Jebelean, J. Mawhin; The Dirichlet problem with mean curvature operator in Minkowski space-a variational approach, Adv.", "mime": "application/pdf"}, {"id": "ejde-795", "words": "18843", "extension": ".pdf", "flesch": "79", "author": "Artes, Joan C.; Llibre, Jaume; Schlomiuk, Dana; Vulpe, Nicolae", "title": "Abel quadratic differential systems of second kind", "date": "2024", "keywords": "case; condition; invariant; picture; siv; systems; t4 =", "summary": "Moreover we detect that the slope of the line is greater than the slope of the flow on the line, because we have SlL \u2212 f \u2212 \u221a 1\u2212 4b \u221a f2 \u2212 4b 2b = ( \u221a 1\u2212 4b+ 1)( \u221a f2 \u2212 4b\u2212 f) 4b > 0. = (h+ 1)xy, y\u0307 = \u2212 f2 (h\u2212 1)2 + fy \u2212 x2 + hy2.", "mime": "application/pdf"}, {"id": "ejde-81", "words": "6719", "extension": ".pdf", "flesch": "84", "author": "huy, Le Thi", "title": "Asymptotic behavior of solutions to 3D Kelvin-Voigt-Brinkman-Forchheimer equations with unbounded delays", "date": "2022", "keywords": "equations; solution", "summary": "\u2212 \u03c6(\u03b8\u2016 \u2264 \u2016Pm\u03c6(\u03b8m) It is easy to check that if u, v, w \u2208 V , then b(u, v, w) = \u2212b(u,w, v), and in particular, b(u, v, v) = 0, \u2200u, v \u2208 V. (2.2) Using Ho\u0308lder\u2019s inequality and Ladyzhenskaya\u2019s inequality, we can choose the best positive constant c0 such that |b(u, v, w)| \u2264 c0\u2016u\u2016\u2016v\u2016|w|1/2\u2016w\u20161/2, \u2200u, v, w \u2208 V. (2.3) From (2.3) and using Poincare\u0301\u2019s inequality (2.1), we obtain |b(u, v, w)| \u2264 c0\u03bb\u22121/4 1 \u2016u\u2016\u2016v\u2016\u2016w\u2016, \u2200u, v, w \u2208 V. (2.4) 4 L. T. THUY EJDE-2022/07 We will assume that f \u2208 L2(0, T ;V \u2032).", "mime": "application/pdf"}, {"id": "ejde-811", "words": "6401", "extension": ".pdf", "flesch": "90", "author": "Li, Chunhong; Zhou, Tiantian", "title": "Discrete Stein-Weiss inequalities", "date": "2025", "keywords": "0,n; j\u2208zn", "summary": "When we cut off f = (fi)i\u2208Zn N and g = (gi)i\u2208Zn N , inequality (1.3) is reduced to\u2211 |i|\u2264N,|j|\u2264N,i\u0338=j |fi||gj | |i\u2212 j|\u03bb \u2264 KN\u2225f\u2225lr(Zn N )\u2225g\u2225ls(Zn N ), \u2200(f, g) \u2208 lr(Zn N )\u00d7ls(Zn N ), (1.4) where KN \u2208 (0,\u221e) is the best constant, and Zn N := {i \u2208 Zn; |i| \u2264 N}. Denote the extremal sequences of (1.13) by (fN , gN ) and |fN i1 | = max{|fN i |; |i| \u2264 N}, |gNi2 | = max{|gNi |; |i| \u2264 N} We write a(N)", "mime": "application/pdf"}, {"id": "ejde-816", "words": "9704", "extension": ".pdf", "flesch": "83", "author": "Baladi, Houssam; Aglzim, Abdellatif; Filali, Mohammed; Tsouli, Najib", "title": "Multiple solutions for p(x)-Kirchhoff type problems with extended Robin boundary conditions", "date": "2024", "keywords": "dx+ \u222b; d\u03c3x; g(x; p(x; \u03b2(x; \u2212 \u222b; \u222b \u03c9", "summary": "+G(x, u) ) d\u03c3x ) div ( |\u2207u|p(x)\u22122\u2207u ) = f(x, u) + \u03bbh(x), x \u2208 \u2126, |\u2207u|p(x)\u22122 \u2202u \u2202\u03bd + \u03b2(x)|u|p(x)\u22122u+ g(x, u) = 0, x \u2208 \u2202\u2126, (1.1) where \u2126 is a bounded domain in RN with smooth boundary \u2202\u2126, \u2202u \u2202\u03bd is the outer normal derivative, d\u03c3x is the measure on the boundary \u2202\u2126, \u03b2 \u2208 L1(\u2202\u2126), \u03b2\u2212 := infx\u2208\u2202\u2126 \u03b2(x) > 0, g : \u2202\u2126 \u00d7 R \u2192 R is a measurable function, with G(x, t) :=\u222b t 0 g(x, s) ds, p \u2208 C+(\u2126\u0304), 1 < p\u2212 := inf x\u2208\u2126\u0304 p(x) \u2264 p+ := max x\u2208\u2126\u0304 p(x) < = o ( |t|\u03b1p+\u22121 ) , t\u2192 0, uniformly a.e. x \u2208 \u2126; (A5) There exists a constant \u00b5 > \u03b1p+ such that \u00b5F (x, t) := \u00b5 \u222b t 0 f(x, s) ds \u2264 f(x, t)t, \u2200(x, t) \u2208 \u2126\u00d7 R; (A6) inf{x\u2208\u2126;|t|=1} F (x, t) > 0. (A7) g(x, t) = o(|t|r1(x)\u22121) uniformly a.e. x \u2208 \u2202\u2126, as t\u2192 0, where r1 \u2208 C+(\u2202\u2126), supx\u2208\u2202\u2126 r1(x) = r+1 < p\u2212 \u2264 p(x) for all x \u2208 \u2202\u2126; (A8) g(x, t) = o ( |t|r2(x)\u22121 ) , t\u2192 +\u221e, uniformly a.e. x \u2208 \u2202\u2126, where r2 \u2208 C+(\u2202\u2126), supx\u2208\u2202\u2126 r2(x) = r+2 < p\u2212 \u2264 p(x) for all x \u2208 \u2202\u2126; (A9) G(x, t) := \u222b t 0 g(x, s) ds \u2265 0, \u2200(x, t) \u2208 \u2202\u2126\u00d7 R, where \u03b1 and \u00b5 are given in (A1) and (A5).", "mime": "application/pdf"}, {"id": "ejde-817", "words": "5138", "extension": ".pdf", "flesch": "70", "author": "Shpakivskyi, Vitalii", "title": "Construction of solutions to PDEs using holomorphic functions of several variables", "date": "2024", "keywords": "equation; functions; holomorphic; variables", "summary": "Holomorphic functions of several complex variables; holomorphic functions of several hypercomplex variables; harmonic algebra; elliptic PDE. (6.4) The general solution of equation (6.4) is the function f(\u03c6,\u03c8, \u03b7) = \u222b\u222b g(\u03c6,\u03c8, \u03b7)d\u03c6d\u03c6+ \u03c6h1(\u03c8, \u03b7) + h2(\u03c8, \u03b7), where h1, h2 are arbitrary holomorphic functions in the domain Q2 := {(\u03c8, \u03b7) \u2208 C2 : (x, y, z) \u2208 \u2126}.", "mime": "application/pdf"}, {"id": "ejde-82", "words": "6199", "extension": ".pdf", "flesch": "81", "author": "Feng, Meiqiang; Chen, Haiping", "title": "Existence and nonexistence of positive solutions for fourth-order elliptic problems", "date": "2023", "keywords": "g(x", "summary": "New criteria for the existence and nonexistence of positive solution are established under some sublinear conditions which involve the principal eigenvalues of the corresponding linear problems. [23] used a variant version of Mountain Pass Theorem to demonstrate the existence and nonexistence of positive solution for the fourth-order elliptic prob- lem \u22062u = f(x, u) in \u2126, u = \u2206u = 0 on \u2202\u2126, where \u2126 denotes a smooth bounded domain in Rn (n > 4).", "mime": "application/pdf"}, {"id": "ejde-823", "words": "4831", "extension": ".pdf", "flesch": "76", "author": "Purushothaman, Ganesh ; Suresh, Kannan ; Thandapani, Ethiraju ; Tunc, Ercan", "title": "Existence and bounds for Kneser-type solutions to noncanonical third-order neutral differential equations", "date": "2024", "keywords": "differential; equations", "summary": "Assuming (3.1) and (3.2), we define G such that for t \u2265 t2, 0 < G(t) if \u03c4(t) \u2264 t, 1\u2212 p(t)R12(\u03c4(t)) R12(t) Q12(\u03c4(t)) Q12(t) if \u03c4(t) \u2265 t, (3.3) Assuming (3.1), we define G1 such that for t \u2265 t2, 0 < G1(t)", "mime": "application/pdf"}, {"id": "ejde-83", "words": "6277", "extension": ".pdf", "flesch": "86", "author": "Shen, Xuhui; Ding, Juntang", "title": "Blow-up for parabolic equations in nonlinear divergence form with time-ependent coefficients", "date": "2022", "keywords": "p\u22121; \u222b \u03c9", "summary": "xj \u2212 k(t)f(u) in \u2126 \u00d7 (0, t\u2217), n\u2211 i,j=1 aij(x)uxi\u03bdj = g(u) on \u2202\u2126 \u00d7 (0, t\u2217), u(x, 0) = u0(x) \u2265 0 in \u2126, where \u2126 is a bounded convex domain in Rn (n \u2265 2) with smooth boundary \u2202\u2126. By constructing suitable auxiliary functions and using a differential inequality technique, when \u2126 \u2282 Rn (n \u2265 2) Published January 25, 2022. 1 2 X. SHEN, J. DING EJDE-2022/08 ( h(u) ) t = n\u2211 i,j=1 ( aij(x)uxi ) xj \u2212 k(t)f(u) in \u2126\u00d7 (0, t\u2217), n\u2211 i,j=1 aij(x)uxi \u03bdj = g(u) on \u2202\u2126\u00d7 (0, t\u2217), u(x, 0) = u0(x) \u2265 0 in \u2126, (1.1) where \u2126 is a bounded convex domain in Rn (n \u2265 2) with smooth boundary \u2202\u2126, (aij(x))n\u00d7n is a differentiable positive definite matrix, \u03bd is the outward normal vector to \u2202\u2126, u0(x) is the initial value, t\u2217 is the maximal existence time of u, and \u2126 is the closure of \u2126. Set R+ = (0,+\u221e).", "mime": "application/pdf"}, {"id": "ejde-84", "words": "4880", "extension": ".pdf", "flesch": "79", "author": "Ferreira, Jorge; Piskin, Erhan; Shahrouzi, Mohammad; Cordeiro , Sebastiao; Raposo, Carlos Alberto", "title": "Existence of global weak solutions for a p-Laplacian inequality with strong issipation in noncylindrical domains", "date": "2022", "keywords": "1,p", "summary": "Let f \u2208 L2(0, T, L2(\u2126t)), u0 \u2208 W 1,p 0 (\u21260), u1 \u2208 L2(\u21260) \u2229K, with K being a convex and closed subset of W 1,p 0 (\u2126), and 0 \u2208 K. Lets us suppose that (H1) and (H2) are satisfied. To this end, let u\u03030 \u2208 W 1,p 0 (\u2126), u\u03031 \u2208 L2(\u2126), and f\u0303 \u2208 L2(Q0) be the extensions to zero outside \u21260 of u0, u1, and f , respectively.", "mime": "application/pdf"}, {"id": "ejde-846", "words": "6614", "extension": ".pdf", "flesch": "78", "author": "Corcho, Adan J.; Mallqui, Lindolfo P.", "title": "L^2 Solutions for cubic NLS equation with higher order fractional\u00a0elliptic/hyperbolic operators on R cross T and \u00a0R^2", "date": "2025", "keywords": "case; |n|2\u03b1", "summary": "First note that S\u03032 = 4 \u230a(C+K) 1 2\u03b1 \u230b\u2211 n=\u230aC 1 2\u03b1 \u230b+1 \u221a C +K \u2212 n2\u03b1 \u2264 4 \u221a K + \u222b \u230a(C+K) 1 2\u03b1 \u230b \u230aC 1 2\u03b1 \u230b+1 \u221a C +K \u2212 z2\u03b1dz \u2264 4 \u221a K + \u222b (C+K) 1 2\u03b1 C 1 2\u03b1 \u221a C +K \u2212 z2\u03b1dz \u2264 4 \u221a K + \u221a K ( (C +K) 1 2\u03b1 \u2212 C 1 2\u03b1 ) . Considering the nonlinear change of variables \u03c12\u03b1 = z2\u03b1 \u2212 C, and using that \u03b1 > 1, C > 0 and K \u2265 1, we have J2 = K \u222b \u221e K 1 2\u03b1 \u03c12\u03b1\u22121 \u03c1\u03b1 ( \u03c12\u03b1 + C )1\u2212 1 2\u03b1 d\u03c1 \u2264 K \u222b \u221e K 1 2\u03b1 \u03c1\u2212\u03b1d\u03c1 = 1 \u03b1\u2212 1 KK 1\u2212\u03b1 2\u03b1 \u2272\u03b1 K. (2.17) Then, inserting (2.17) in (2.16) one obtains S\u2212 2 \u2272\u03b1 K. Therefore, from (2.14) and the estimates obtained for S\u2212 1 and S\u2212 2 we have m ( G\u2212 1,K ) \u2272\u03b1 K. By the same way we have m ( G\u2212 2,K ) \u2272\u03b1 K. So, m ( G\u2212 K )", "mime": "application/pdf"}, {"id": "ejde-85", "words": "9013", "extension": ".pdf", "flesch": "83", "author": "Wen, Lan; Yang, Lu", "title": "Dynamics of a non-autonomous stochastic weakly damped plate model with critical exponent", "date": "2022", "keywords": "\u03b8\u2212\u03c4\u03c9", "summary": "(4.29) Let T = T1 = 4c45K0 \u03c31\u03b5 in (4.18), for \u03c4 \u2212 t \u2264 r \u2264 \u03c4 , we have\u222b \u03c4 r \u2016w1(s)\u2016q\u22121 2 ds \u2264 \u03b5 4c45 (\u03c4 \u2212 r) + = ( u(t+ \u03c4, \u03c4, \u03b8\u2212\u03c4\u03c9, \u03d5\u03c4 (\u03b8\u2212\u03c4\u03c9)) ut(t+ \u03c4, \u03c4, \u03b8\u2212\u03c4\u03c9, \u03d5\u03c4 ) + \u03b5u(t+ \u03c4, \u03c4, \u03b8\u2212\u03c4\u03c9, \u03d5\u03c4 )\u2212 h(x)z(\u03b8t\u03c9) ) over R and (\u2126,F ,P, (\u03b8t)t\u2208R), where \u03a6(0, \u03c4, \u03c9)\u03d5\u03c4 (\u03c9) = \u03d5\u03c4 (\u03b8\u2212\u03c4\u03c9) and \u03a6(t, \u03c4 \u2212 t, \u03b8\u2212t\u03c9)\u03d5\u03c4\u2212t(\u03b8\u2212t\u03c9) = \u03d5(\u03c4, \u03c4 \u2212 t, \u03b8\u2212\u03c4\u03c9, \u03d5\u03c4\u2212t(\u03b8\u2212\u03c4\u03c9)).", "mime": "application/pdf"}, {"id": "ejde-850", "words": "4829", "extension": ".pdf", "flesch": "77", "author": "Doan, Thai Son Doan; Huong, Phan Thi; Kloeden, Peter E.", "title": "theta-scheme for solving Caputo fractional differential equations", "date": "2025", "keywords": "scheme", "summary": "Write Y (n) k = Y (n)(kTn ) with Y (n) 0 = y0. , n\u2212 1, which gives Y (n) 1 = Y (n) 0 + f(t0, Y (n) 0 ) T n , Y (n) 2 = Y (n) 0 + f(t0, Y (n) 0 ) T n + f(t1, Y (n) 1 ) T n = Y (n) 1 + f(t1, Y (n) 1 ) T n , and so on, culminating in Y (n) k+1 = Y (n) k + f(tk, Y (n) k ) T n .", "mime": "application/pdf"}, {"id": "ejde-856", "words": "7840", "extension": ".pdf", "flesch": "75", "author": "Agarwal, Ravi ; Baltaeva, Umida; Hubert, Florence; Khasanov, Boburjon ", "title": "Existence and uniqueness of \u00a0the solution to initial and inverse problems for\u00a0integro-differential heat equations with fractional load", "date": "2024", "keywords": "a(\u03b8\u22121(\u03c4; equation; fractional; inverse; problem; t 0; \u222b rn; \u222b \u03b8(t; \u222b \u03b8\u22121(\u03c4", "summary": "Fractional diffusion equations are extensions of the basic equations of mathe- matical physics Find a solution u(x, t) in the domain (x, t) \u2208 Rn T of the loaded heat equation ut \u2212 a(t)\u2206u = \u03bbD\u2212\u03b1 0t u(x \u2032, t) + \u222b t 0 k(x\u2032, \u03c4)u(x, t\u2212 \u03c4)d\u03c4, (x, t) \u2208 Rn T , (2.1) that satisfies the condition u(x, t) \u2223\u2223 t=0 = \u03c6(x), x \u2208 Rn, (2.2) where D\u2212\u03b1 0t is the Riemann-Liouville fractional integral operator of order \u03b1 defined by D\u2212\u03b1 0t u(x \u2032, t)", "mime": "application/pdf"}, {"id": "ejde-86", "words": "6384", "extension": ".pdf", "flesch": "76", "author": "Hao, Jianghao; Yang, Jing", "title": "Exponential stability for porous thermoelastic systems with Gurtin-Pipkin flux", "date": "2023", "keywords": "stability; system; \u222b \u221e", "summary": "\u03c1v \u2212 \u00b5uxx \u2212 b\u03d5x \u2212 \u03b3vxx = \u03c1f2, (3.6) \u03d5\u2212 w = f3, (3.7) Introduction In this work, we consider the porous thermoelastic transmission system with Gurtin-Pipkin flux, \u03c1utt \u2212 \u00b5uxx \u2212 b\u03d5x \u2212 \u03b3uxxt = 0 in (0, 1)\u00d7 R+, J\u03d5tt \u2212 \u03b4\u03d5xx + bux + \u03be\u03d5+ \u03b2\u03b8x", "mime": "application/pdf"}, {"id": "ejde-860", "words": "4667", "extension": ".pdf", "flesch": "85", "author": "Figueiredo, Giovany M.; Kiametis, George", "title": "Caffarelli-Kohn-Nirenberg type problems with Berestycki-Lions type nonlinearities", "date": "2024", "keywords": "lemma; |x|\u2212bp\u2217", "summary": "Let u \u2208 Erad, then for almost every x \u2208 RN\\{0}, then there exists C = C(a, b, p) > 0 such that |u(x)| \u2264 C 1 |x| (N\u2212p)\u2212ap\u2217 p \u2225u\u2225. Proof. Hence, there exists u \u2208 Erad such that, up to a subsequence, un \u21c0 u in Erad.", "mime": "application/pdf"}, {"id": "ejde-87", "words": "10373", "extension": ".pdf", "flesch": "90", "author": "Zhang, Bo; Liu, Xiangqing", "title": "Localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth", "date": "2022", "keywords": "1,p(rn; choquard; dx dy; equations; k\u03b5(x; lemma; y|\u03b1; |x\u2212; \u222b rn", "summary": "2\u2212p 2 \u2264 c (\u222b RN (|\u2207uk|p\u22122\u2207uk \u2212 |\u2207ul|p\u22122\u2207ul,\u2207uk \u2212\u2207ul) dx )p/2 \u2192 0, as k, l\u2192\u221e, \u222b RN E(\u03b5x)|uk \u2212 ul|p dx \u2264 c (\u222b RN (|uk|p\u22122uk \u2212 |ul|p\u22122ul)(uk \u2212 ul) dx )p/2 \u00d7 (\u222b RN (|uk|p + |ul|p) dx ) 2\u2212p 2 \u2264 c (\u222b RN (|uk|p\u22122uk \u2212 |ul|p\u22122ul)(uk \u2212 ul) dx )p/2 \u2192 0, as k, l\u2192\u221e and \u222b RN exp{(m\u2212 p) dist(\u03b5x,M)}|(uk \u2212 ul)|m dx \u2264 c (\u222b RN (k\u03b5(x, uk)\u2212 k\u03b5(x, ul))(uk \u2212 ul) dx )m/2 \u00d7 (\u222b RN \u03b5m\u2212p exp{(m\u2212 p) dist(\u03b5x,M)}(|uk|m + |ul|m) dx ) 2\u2212m 2 \u2264 c ( \u222b RN (k\u03b5(x, uk)\u2212 k\u03b5(x, ul))(uk \u2212 ul) dx )m/2 \u2192 0, as k, l\u2192\u221e. So {un} is a Cauchy sequence in X\u03b5. \ufffd 10 B. ZHANG, X. LIU EJDE-2022/11 3.", "mime": "application/pdf"}, {"id": "ejde-88", "words": "8744", "extension": ".pdf", "flesch": "81", "author": "Mishra, Indira", "title": "Homogenization of boundary optimal control problem", "date": "2022", "keywords": "boundary; control; problems; \u03c9\u00d7y", "summary": "Let Y , T and Y \u2217 be as follows: Y = (0, 1)N is a reference cell, or more generally a set having the paving property with respect to a basis (b1, . . = 0 in Y \u2217, A(x, y)[\u2207y\u00b5i(x, y) + ei] \u00b7 \u03bd = 0 on \u2202Y \u2217\\\u2202Y, y 7\u2192 \u00b5i(x, y) is Y -periodic.", "mime": "application/pdf"}, {"id": "ejde-881", "words": "8631", "extension": ".pdf", "flesch": "72", "author": "Zhang, Xiang; Kang, Ming; Geng, Fengjie", "title": "Dynamic behavior of a stochastic predator-prey model with stage-structure and nonlinear perturbation", "date": "2025", "keywords": "+ \u03c32; predator; prey; \u03c311\u03c312d2", "summary": "= \u2212 lnx1 \u2212 lnx2. 6 X. ZHANG, M. KANG, F. GENG EJDE-2025/32 Combining (3.1) and (3.2), we have LV1 = \u2212r x2 x1 + \u03b1y +m+ d1 + (\u03c311 + \u03c312x1) 2 2 \u2212m x1 x2 + sx2 + \u03b2y (1 + ax2)(1 + by) + d2 + (\u03c321 + \u03c322x2) 2 2 \u2264 \u2212rx2 x1 \u2212 mx1 x2 + \u03b1y +m+ d1 + \u03c32 11 2 + \u03c311\u03c312x1 + \u03c32 12 2 x2 1 + sx2 + \u03b2 b + d2 + \u03c32 21 + \u03c32 22x 2 2 \u2264 ( \u22122 \u221a rm+m+ d1 + \u03b2 b + d2 + \u03c32 11 2 + \u03c32 21 ) + \u03b1y + \u03c311\u03c312x1 + \u03c32 12 2 x2 1 + sx2 + \u03c32 22x 2 2. (3.3) We define V2(x1) = u1(x1 + u2) v v , where u1 and u2 are positive constants which will be determined later, v \u2208 (0, 1) is adequately small. +mx1( 1 \u221a x2 \u2212 1 x2 )\u2212 \u03c32 12x 5 2 1 4 + \u03c32 12x 2 1 + p\u03b1 2 x2 1 \u2212 \u03c32 22x 5 2 2 4 + \u03c32 22x 2 2 + sx2 + q\u03b2 2 x2 2 \u2212 \u03c32 32y 5 2 4 + \u03b1y + p\u03b1 2 y + q\u03b2 2 y + \u03b4y + \u03c32 32y 2 +m 4 X. ZHANG, M. KANG, F. GENG EJDE-2025/32 + d1 + d2 + d3 + \u03b2 b + \u03c32 11 + \u03c32 21 + \u03c32 31 \u2264 rx2 4 + mx1 4 \u2212 \u03c32 12x 5 2 1 4 + \u03c32 12x 2 1 + p\u03b1 2 x2 1 \u2212 \u03c32 22x 5 2 2 4 + \u03c32 22x 2 2 + sx2 + q\u03b2 2 x2 2 \u2212 \u03c32 32y 5 2 4 + \u03b1y + p\u03b1 2 y + q\u03b2 2 y + \u03b4y + \u03c32 32y 2 +m+ d1 + d2 + d3 + \u03b2 b + \u03c32 11 + \u03c32 21 + \u03c32 31 = ( \u2212\u03c32 12x 5 2 1 4 + \u03c32 12x 2 1 + p\u03b1 2 x2 1 + mx1 4 )", "mime": "application/pdf"}, {"id": "ejde-885", "words": "5895", "extension": ".pdf", "flesch": "53", "author": "Gerberry, David; Joshi, Hem; Peloquin, Mac; Vargas, Sonia", "title": "Respiratory Illness clinical trial modeling", "date": "2024", "keywords": "adults; children; days; kids; population; trial; vaccine; wave", "summary": "Of course, it is important to note that vaccine clinical trials do not occur in a vacuum but rather involve individuals (both in the control and treatment arms of the clinical trial) interacting with the general population under the current condi- tions of the epidemic. General simulation linking epidemiological dynamics to those of vaccine clinical trials in adults and children.", "mime": "application/pdf"}, {"id": "ejde-886", "words": "6193", "extension": ".pdf", "flesch": "88", "author": "Kimura, Yasunori; Sasaki, Kazuya; Torii, Kakeru", "title": "Convergence theorems of implicit type iterations in geodesic spaces with negative curvature", "date": "2024", "keywords": "cosh; d(xn", "summary": "For x, y \u2208 X and l \u2265 0, a mapping c : Then, we denote the image of the geodesic with endpoints x, y \u2208 X by [x, y], which is well defined.", "mime": "application/pdf"}, {"id": "ejde-887", "words": "10173", "extension": ".pdf", "flesch": "61", "author": "Ludu, Andrei; Khanal, Harihar; Carstea, Adrian Stefan", "title": "Nonlinear non-autonomous Boussinesq equations", "date": "2024", "keywords": "amplitude; boussinesq; case; coefficient; equations; nonlinear; numerical; soliton; solutions; system; variable; waves", "summary": "Boussinesq non-autonomous nonlinear system We consider a non-autonomous and nonlinear Boussinesq-type of differential system in the form qzt + (qu+ \u03b1zu)x + \u03b2 3 (qu)xxx = 0, qut + zx + \u03b1uux = 0, (2.1) for the solutions z(x, t), u(x, t) where (x, t) \u2208 (\u2212L,L)\u00d7[0,\u221e) and the space domain can be arbitrary extended L to\u221e. Subscripts x, t represent differentiation. Boussinesq non-autonomous nonlinear system 2.1.", "mime": "application/pdf"}, {"id": "ejde-888", "words": "5554", "extension": ".pdf", "flesch": "74", "author": "Sharma, Anshul; Mishra, Suyash Narayan; Shukla, Anurag", "title": "Asymptotic stability for Hilfer-like nabla nonlinear fractional difference equations", "date": "2024", "keywords": "difference; fractional; stability; \u03b7(\u03c9", "summary": "We examined the existence and uniqueness theorem, asymptotic sta- bility of fractional nonlinear difference equations. Hilfer-like nabla operator; asymptotic stability; fractional difference equations; Lyapunov direct method.", "mime": "application/pdf"}, {"id": "ejde-889", "words": "4875", "extension": ".pdf", "flesch": "68", "author": "Tarfulea, Nicoleta E.", "title": "On drug therapy for an HIV infection age model with cellular and immune delays", "date": "2024", "keywords": "cell; hiv; infection; model; virus", "summary": "There have been a variety of modifications of HIV mathematical models that have resulted from incorporating drug therapies. Without treatment with HIV medicines, HIV infection advances in stages, getting worse over time.", "mime": "application/pdf"}, {"id": "ejde-890", "words": "8317", "extension": ".pdf", "flesch": "66", "author": "Verma, Vijai Shanker; Kunwar, Laxman Bahadur", "title": "Impact of vaccination and sterilization on the transmission dynamics of rabies", "date": "2024", "keywords": "dogs; equilibrium; human; model; population; rabies", "summary": "Based on the parameter val- ues listed in the Table 2, we have used model (1.1)-(1.2) to simulate the data and we predicted the trend of exposed to rabies human population in Nepal. Thus, with the current control and prevention measures, dog and human rabies will persist endemically, which is also justified in Figure 3. 3.2.", "mime": "application/pdf"}, {"id": "ejde-897", "words": "5350", "extension": ".pdf", "flesch": "75", "author": "Huang, Rui; Ji, Shanming; Ma, Yansheng", "title": "Cauchy problem for the Lane-Emden heat flow with sign-changing initial data", "date": "2024", "keywords": "u(x; \u03c9\u0302+", "summary": "Comparison principle of the heat equation implies that u(x, t) \u2265 u(x) for t \u2208 (0, Tmax), which means that \u2126\u0302+ u0 \u2282 \u2126+ u(x,t) and \u2126\u2212 u(x,t) \u2282 v(x)dx \u2265 (1\u2212 \u03b11\u2212p) (\u222b \u2126\u0302+ u0 u+(x, t) \u00b7 v(x)dx )p(\u222b \u2126\u0302+ u0 v(x)dx )1\u2212p = (1\u2212 \u03b11\u2212p) \u00b7 (\u222b \u2126\u0302+ u0 v(x)dx )1\u2212p zp(t), t \u2208 (\u03c4, Tmax), (2.10) which implies that z(t) blows up in finite time since p > 1 and z(\u03c4) > 0. \u25a1 Proof of Theorem 1.1.", "mime": "application/pdf"}, {"id": "ejde-902", "words": "4791", "extension": ".pdf", "flesch": "59", "author": "Salwahan, Shraddha; Abbas, Syed; Tridane, Abdessamad", "title": "Optimal switching of vaccination for an infectious disease model", "date": "2024", "keywords": "control; disease; model; switching; system; vaccination", "summary": "Finally, some numerical simulations are performed to compare continuous vaccination programs and optimal switching of vaccination control. Hence, the system switches between two subsystems according to the presence of vaccination control.", "mime": "application/pdf"}, {"id": "ejde-911", "words": "9720", "extension": ".pdf", "flesch": "87", "author": "Bai, Ruobing; Saanouni, Tarek", "title": "Non global solutions for non-radial inhomogeneous nonlinear Schrodinger equations", "date": "2025", "keywords": "schro\u0308dinger; |u|p; |\u2212\u03c4", "summary": "|\u2212\u03c4 |u|p ) |x|\u2212\u03c4 |u|p dx ) + 8 p (\u2212\u03c4 \u2212 N \u2212 \u03b1 2 ) \u222b RN ( J\u03b1 \u2217 | \u00b7 = ( ( A B )1\u2212 B 2 (M[\u03c6])p\u22121(M[u0]) \u2212A/2 ) 2 B\u22122 ( 1\u2212 2 B ) = B \u2212 2 A ( (M[u0]) \u2212A/2(M[\u03c6])p\u22121 ) 2 B\u22122 = B \u2212 2 A ( M[u0] )\u2212\u03b1c ( M[\u03c6] )2/sc . (3.67) Relations (3.66) and (3.67) imply that E [u0] < F (x1).", "mime": "application/pdf"}, {"id": "ejde-92", "words": "5072", "extension": ".pdf", "flesch": "78", "author": "Sabina de Lis, Jose C.", "title": "Remarks on the second Neumann eigenvalue", "date": "2022", "keywords": "eigenvalue", "summary": "In the first one, X = \u2126 is a bounded set of Rn, endowed with the measure d\u00b5 = m(x)dx where m \u2208 L1(\u2126), m(x) > 0 if 1 < p < N, > 1 if p = N, = 1 if p > N. We define \u03bb\u0302(m) = inf u\u2208M0\\{0} \u222b \u2126 |\u2207u|p dx\u222b \u2126 |u|pmdx , (3.1) with M0 = {u \u2208 W 1,p(\u2126) : \u222b \u2126 |u|p\u22122umdx = 0}.", "mime": "application/pdf"}, {"id": "ejde-931", "words": "7550", "extension": ".pdf", "flesch": "81", "author": "Qiu, Ruowen; You, Renqing; Zhao, Fukun", "title": "Infinitely many sign-changing solutions for an asymptotically linear and nonlocal schrodinger equation", "date": "2025", "keywords": "f(x; lemma", "summary": "Indeed, if 0 \u2208 I(W \u2229 \u2202M), then there exists u \u2208 W \u2229 \u2202M such that \u222b RN F (x, u+) dx =\u222b RN F (x, u\u2212) dx. Now, we choose {yn} \u2282 RN such that RN \u2282 \u22c3\u221e i=1 Br(yi) and each x \u2208 RN is covered by at most 2N balls.", "mime": "application/pdf"}, {"id": "ejde-932", "words": "5132", "extension": ".pdf", "flesch": "82", "author": "Chen, Kai; Wang, Jinrong", "title": "Ulam type stability for nonlinear Hahn difference equations with delay", "date": "2024", "keywords": "equation; stability; ulam", "summary": "Secondly, we examine the equation D2 q,\u03c9x(s) = F (s, x(s),Dq,\u03c9x(s), x(\u0398(s))), s \u2208 I1, x(s) = y(s), Dq,\u03c9x(s) = Dq,\u03c9y(s), s \u2208 I2, (1.2) where F : I1 \u00d7 R3 \u2192 R is continuous at s = \u03c90. ,D n\u22121 q,\u03c9 x(s), x(\u0398(s))), s \u2208 I1, x(s) = y(s), Dj q,\u03c9x(s) =", "mime": "application/pdf"}, {"id": "ejde-942", "words": "7207", "extension": ".pdf", "flesch": "62", "author": "Zhang, Sen; Zu, Jian; Zhang, Jingqi", "title": "Deep learning method for finding eigenpairs in Sturm-Liouville eigenvalue problems", "date": "2024", "keywords": "boundary; eigenpairs; eigenvalue; liouville; method; problems; sturm", "summary": "It is not difficult to know that \u03b8\u2032 = \u221a \u039bk \u2212 \u03c10 \u2212 (\u03b7u(x)\u2212 \u03c10) sin 2 \u03b8\u221a \u039bk \u2212 \u03c10 \u2264 \u221a \u039bk \u2212 \u03c10. |\u039bj \u2212 \u039bk| \u2212 |\u03bbk \u2212 \u039bk| \u2265 |j2 + \u03c10 \u2212 k2 \u2212 \u03c11| \u2212 |k2 + \u03c11 \u2212 k2 \u2212 \u03c10| \u2265 |j2 \u2212 k2| \u2212 2|\u03c11 \u2212 \u03c10| \u2265 1.", "mime": "application/pdf"}, {"id": "ejde-955", "words": "8303", "extension": ".pdf", "flesch": "77", "author": "Ma, Wenhui; Ma, Qiaozhen", "title": "Random attractors and their stability for nonclassical diffusion equations driven by additive white noise with delay and intensity", "date": "2025", "keywords": "h1(rn; \u2208 r", "summary": "Then for every \u03c4 \u2208 R, \u03c9 \u2208 \u2126, \u03f5 \u2208 (0, 1] and D = {D(\u03c4, \u03c9) : \u03c4 \u2208 R, \u03c9 \u2208 \u2126} \u2208 D, the solution of problem (3.4)-(3.5) satisfies \u2225 d dt v(t, \u03c4 \u2212 t, \u03b8\u2212\u03c4\u03c9, \u03c8)\u22252H1(Rn) \u2264 Q1(\u2225v(t, \u03c4 \u2212 t, \u03b8\u2212\u03c4\u03c9, \u03c8)\u22252H1(Rn) + \u2225g(t)\u22252 + \u03f5|y(\u03b8t\u2212\u03c4\u03c9)|2 + \u2225u(t\u2212 \u03c1, \u03c4 \u2212 t, \u03b8\u2212\u03c4\u03c9, \u03d5)\u22252H1(Rn) + 1), (4.14) where Q1 > 0 is a constant independent of \u03c4, \u03c9,D and \u03c8 \u2208 D(\u03c4 \u2212 t, \u03b8\u2212t\u03c9). Proof. Then for every \u03c4 \u2208 R, \u03c9 \u2208 \u2126, s \u2208 [\u2212\u03c1, 0], D = {D(\u03c4, \u03c9) : \u03c4 \u2208 R, \u03c9 \u2208 \u2126} \u2208 D and \u03c8 \u2208 D(\u03c4 \u2212 t, \u03b8\u2212t\u03c9), the solution of problem (3.4)-(3.5) satisfies lim k,t\u2192+\u221e \u222b Oc k \u2225v(\u03c4 + s, \u03c4 \u2212 t, \u03b8\u2212\u03c4\u03c9, \u03c8)\u22252H1(Rn)dx = 0. (4.22) Proof.", "mime": "application/pdf"}, {"id": "ejde-96", "words": "12468", "extension": ".pdf", "flesch": "87", "author": "Melzi, Imane; Atik, Youcef", "title": "A nonlinear mathematical model for two-phase flow in nanoporous media", "date": "2022", "keywords": "dx dt; s\u03b1(x; \u2212 \u222b; \u222b \u03c9", "summary": "For 1 \u2264 p < \u221e and B a Banach space, we denote Lp(I;B) the Bochner space (of classes with respect to equiva- lence a.e.) of Bochner integrable functions u : I \u2212\u2192 B satisfying \u222b T 0 \u2016u(t)\u2016pB dt < +\u221e. , N, (4.2) \u222b T 0 (\u03c6\u2202\u2212\u03b1t s\u03b1, \u03c8) dt+ \u222b \u2126T \u03bbw(s\u03b1)K(\u2207p\u03b1)\u2207p\u03b1 \u00b7 \u2207\u03c8 dx dt + \u222b \u2126T \u039b\u03b5(s \u03b1)p\u2032c(s \u03b1)K(\u2207p\u03b1)\u2207s\u03b1 \u00b7", "mime": "application/pdf"}, {"id": "ejde-963", "words": "7873", "extension": ".pdf", "flesch": "75", "author": "Bunoiu, Renata; Ramdani, Karim; Timofte, Claudia", "title": "Asymptotic analysis of \u00a0sign-changing transmission problems with rapidly oscillating interface", "date": "2024", "keywords": "problem", "summary": "[7] A. Bonnet-Ben Dhia, L. Chesnel, P. Ciarlet Jr.; T -coercivity for scalar interface problems between dielectrics and metamaterials, ESAIM Math. Positive and negative materials; transmission problem; asymptotic analysis; oscillating interface; imperfect interfaces; flux jump.", "mime": "application/pdf"}, {"id": "ejde-97", "words": "10642", "extension": ".pdf", "flesch": "85", "author": "Li, Chunyang; Dong, Xiu; Wang, Jinliang", "title": "Stability analysis of an age-structured viral infection model with latency", "date": "2022", "keywords": "infection; t t; t \u2217v; \u03b21 t; \u03b22 t; \u222b \u221e", "summary": "+ \u222b t 0 \u03be(a)\u2126(a)e\u0302(t\u2212 a) da+ \u222b \u221e t \u03be(a) \u2126(a) \u2126(a\u2212 t) e0(a\u2212 t) da. + \u222b t 0 \u03be(a)\u2126(a)e\u0302(t\u2212 a)da. (4.5)", "mime": "application/pdf"}, {"id": "ejde-974", "words": "7060", "extension": ".pdf", "flesch": "86", "author": "Xie, Junhui; Li, Pengfei", "title": "Existence of solutions to fractional p-Laplacian problems with Robin boundary conditions", "date": "2025", "keywords": "|x|\u03b1", "summary": "Hence g\u2032(t) = \u2212tr\u2212p\u22121(r \u2212 q)(r \u2212 p) \u222b \u2126 |u|r |x|\u03b1 dx < 0. On the contrary, ifN0 \u03bb \u0338= \u2205, then there exists u \u2208 N0 \u03bb, this implies \u27e8\u03a8\u2032(u), u\u27e9 = 0, we can deduce that (p\u2212 q)\u2225u\u2225p Xs,p \u03b2 \u2264 (p\u2212 q)\u2225u\u2225p Xs,p \u03b2 + (p\u2212 q) \u222b Rn\\\u2126 \u03b2(x)|u|pdx = (r \u2212 q) \u222b \u2126 |u|r |x|\u03b1 dx, (3.3) EJDE-2025/13 SOLUTIONS TO FRACTIONAL P-LAPLACIAN PROBLEMS 7 and (r \u2212 p)\u2225u\u2225p Xs,p \u03b2 \u2264 (r \u2212 p)\u2225u\u2225p Xs,p \u03b2 + (r \u2212 p) \u222b Rn\\\u2126 \u03b2(x)|u|pdx = (r \u2212 q)\u03bb \u222b \u2126 |u|qdx. (3.4) By (2.2), we obtain (r \u2212 q) \u222b \u2126 |u|r |x|\u03b1 dx \u2264 (r \u2212 q)S\u2212r/p \u03b1 C\u0302\u22121\u2225u\u2225rXs,p \u03b2 .", "mime": "application/pdf"}, {"id": "ejde-984", "words": "8347", "extension": ".pdf", "flesch": "82", "author": "Zhang, Tianqing; Guo, Zhenyu", "title": "Normalized solutions of fractional Kirchhoff equations: the defocusing case", "date": "2025", "keywords": "fractional; p\u03b4s; solutions", "summary": "Setting u \u2208 Pc,\u00b5, by fractional Gagliardo-Nirenberg inequality and \u00b5 < 0 we obtain that a|(\u2212\u2206)s/2u|22 \u2264 \u03b4s,p|u|pp \u2264 \u03b4s,pC(s, p) p| \u2212\u2206s/2u|p\u03b4s,p2 |u|p(1\u2212\u03b4s,p) 2 . (3.26) From the definition of Pc,\u00b5, we obtain u \u2208 Sc, namely, |u|2 = c. Let N \u2265 2, then Hs r (RN ) is compactly embedding into Lp(RN ) for p \u2208 (2, 2\u2217s).", "mime": "application/pdf"}, {"id": "ejde-988", "words": "7035", "extension": ".pdf", "flesch": "80", "author": "Zhang, Xue; Zhao, Xiaopeng", "title": "Strong solutions to density-dependent incompressible smectic-A liquid crystal equations", "date": "2025", "keywords": "inequality; liquid; system", "summary": "\u2225ut\u2225L2 \u2264 \u00b54 28 \u2225\u2207ut\u22252L2 + C(\u2225\u2207\u2206\u03c6t\u22254L2 + \u2225\u2207\u03c6t\u22254L2 + \u2225\u22062\u03c6\u22254L2 + \u2225ut\u22254L2 + 1), (3.39) J24 \u2264 C\u2225\u2207ut\u2225L2\u2225\u2207\u03c6t\u2225L2 \u2264 \u00b54 28 \u2225\u2207ut\u22252L2 + C\u2225\u2207\u03c6t\u22252L2 , (3.40) J25 \u2264 C\u2225\u2206\u03c6t\u2225L2\u2225\u2207\u03c6\u22252L6\u2225ut\u2225L6 \u2264 C\u2225\u2207\u2206\u03c6t\u22251/2L2 \u2225\u2207\u03c6t\u22251/2L2 \u2225\u2207\u03c6\u22252H1\u2225ut\u2225H1 \u2264 \u00b54 28 \u2225\u2207ut\u22252L2 + C\u2225\u2207\u2206\u03c6t\u2225L2\u2225\u2207\u03c6t\u2225L2\u2225\u2207\u03c6\u22254H1 + C\u2225\u2207\u2206\u03c6t\u22251/2L2 \u2225\u2207\u03c6t\u22251/2L2 \u2225\u2207\u03c6\u22252H1\u2225ut\u2225L2 \u2264 \u00b54 28 \u2225\u2207ut\u22252L2 + C(\u2225ut\u22256L2 + \u2225\u2207\u2206\u03c6t\u22256L2 + \u2225\u2207\u03c6t\u22256L2 + \u2225\u2207\u03c6\u22256H1 + 1), (3.41) J26 \u2264 C\u2225\u2207\u03c6t\u2225L2\u2225\u2207\u03c6\u2225L6\u2225\u2206\u03c6\u2225L6\u2225ut\u2225L6 \u2264 C\u2225\u2207\u03c6t\u2225L2\u2225\u2207\u03c6\u22252H2\u2225ut\u2225H1 \u2264 \u00b54 28 \u2225\u2207ut\u22252L2 + C\u2225\u2207\u03c6t\u22252L2\u2225\u2207\u03c6\u22254H2 + C\u2225\u2207\u03c6t\u2225L2\u2225\u2207\u03c6\u22252H2\u2225ut\u2225L2 \u2264 \u00b54 28 \u2225\u2207ut\u22252L2 + C(\u2225\u2207\u2206\u03c6\u22256L2 + \u2225\u2207\u03c6\u22256L2 + \u2225\u2207\u03c6t\u22256L2 + \u2225ut\u22256L2 + 1). Also, \u222b \u2126 |u||\u2207\u03c6||\u03c6|dx \u2264 \u2225u\u2225L3\u2225\u2207\u03c6\u2225L2\u2225\u03c6\u2225L6 \u2264 C\u2225u\u2225H1\u2225\u03c6\u22252H1 \u2264 C(\u2225u\u22253H1 + \u2225\u03c6\u22253H1).", "mime": "application/pdf"}, {"id": "ejde-996", "words": "17719", "extension": ".pdf", "flesch": "73", "author": "Belin, Th\u00e9o; Lafitte, Pauline", "title": "Quantitative estimates of L^p maximal regularity for nonautonomous operators and global existence for quasilinear equations", "date": "2025", "keywords": "bounded; constant; continuity; mrp(i; nonautonomous; operators; regularity; theorem", "summary": "Also for t \u2208 Denote for \u03f5 > 0, E\u03f5 := {t \u2208 I : \u03c1(t) > \u03f5}.", "mime": "application/pdf"}]