id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-452	Wang, Xiaohui; Zhao, Peihao	Existence of weak solutions to superlinear elliptic systems without the Ambrosetti-Rabinowitz condition	2020	21	.pdf	application/pdf	8139	431	81	We first consider the p-Laplacian equation −∆pu = λf(x, u) in Ω, u = 0 on ∂Ω, (1.1) where p > 1, λ > 0, Ω ⊂ Rn is a bounded domain, f : Ω × R → R is a continuous function, and for 1 < p <∞, the p-Laplacian operator is ∆pu = div(|Du|p−2Du) for u ∈W 1,p(Ω). |t|p = +∞ a.e. in Ω, or lim t→−∞ F (x, t) |t|p = +∞ a.e. in Ω. 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.	cache/ejde-452.pdf	txt/ejde-452.txt