id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-147	Wang, Lixia	Localized nodal solutions for semiclassical nonlinear Kirchhoff equations	2022	23	.pdf	application/pdf	9864	483	85	For every 1 ≤ i ≤ mj, ṽi is a nontrivial solution of − (a+ bAj)∆v + V (yij)v = |v|p−2v, v ∈ H1(R3), (4.13) where yij = limε→0 εy i j,ε ∈ Λ̄; (iii) For any 2 < q < 6, lim ε→0 ‖vj,ε − ṽ0 − mj∑ i=1 ṽi(· − yij,ε)‖Lq(R3) = 0. (4.14) Proof. Since vj,ε, ṽ0 and ṽ1 solves (2.4), (4.12), and (4.13) with i = 1 respectively, we have − a∆v2 j,ε − b ∫ R3 |∇vj,ε|2dx∆v2 j,ε − b (∫ R3 |∇vj,ε|2 −Aj ) ∆ṽ0 − b (∫ R3 |∇vj,ε|2 −Aj ) ∆ṽ1 + ξεχεv 2 j,ε + ξεχεṽ0 + ξεχεṽ1 + V (εx)v2 j,ε + (V (εx)− V (0))ṽ0 + (V (εx)− V (yij))ṽ1(· − y1 j,ε) = |vj,ε|p−2vj,ε − |ṽ0|p−2ṽ0 − |ṽ1|p−2ṽ1(· − y1 j,ε).	cache/ejde-147.pdf	txt/ejde-147.txt