On the existence of nontrivial solutions of quasi-asymptotically linear problem for the p-Laplacian

被引：0

作者：

Chen Z.-H. ^{[1
]}

Shen Y.-T. ^{[1
]}

机构：

[1] Department of Applied Mathematics, South China University of Technology

来源：

Acta Mathematicae Applicatae Sinica | 2002年 / 18卷 / 4期

基金：

中国国家自然科学基金;

关键词：

Critical point; Palais-Smale type condition; Quasi-asymptotically linear; Weak solution;

D O I：

10.1007/s102550200062

中图分类号：

学科分类号：

摘要：

In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p > 1): {- Δpu ≡ -div (|∇u| p-2∇u) = f(x, u), x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω is a bounded domain in ℝN (N ≥ 1) and f(x,u) is quasi-asymptotically linear with respect to |u|p-2u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f(x, s)/sp-1 is nondecreasing with respect to s for all x ∈ Ω, and some others. In this paper, by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x, s)/sp-1 isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.

引用

页码：599 / 606

页数：7

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