id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-263	Youssfi, Ahmed; Khatri, Mohamed Mahmoud Ould	Continuous imbedding in Musielak spaces with an application to anisotropic nonlinear Neumann problems	2021	28	.pdf	application/pdf	11725	708	86	, N , we denote by νi the ith component of the outer normal unit vector and ai : Ω × R → R is a Carathéodory function such that there exist a locally integrable Musielak-Orlicz function (see definition 1.1 below) Pi : Ω× R+ → R+ with Pi � φi, a positive constant ci and a nonnegative function di ∈ Eφ∗i (Ω) satisfying for all s, t ∈ R and for almost every x ∈ Ω the following assumptions |ai(x, s)| ≤ ci ( di(x) + (φ∗i ) −1(x, Pi(x, s)) ) , (1.2) φi(x, |s|) ≤ ai(x, s)s ≤ Ai(x, s), (1.3) 2010 Mathematics Subject Classification. × R+ → R+ with R � φmax and a nonnegative function D ∈ Eφ∗max (Ω), such that for all s, t ∈ R and for almost every x ∈ Ω, |ϕmax(x, s)| ≤ D(x) + (φ∗max)−1(x,R(x, s)), (1.5) where φ∗max stands for the complementary function of φmax defined below in (2.1).	cache/ejde-263.pdf	txt/ejde-263.txt