Existence and multiplicity of nontrivial solutions for a class of modified nonlinear fourth-order elliptic equations on RN

被引：23

作者：

Chen, Shaoxiong ^{[1
]}

Liu, Jiu ^{[2
]}

Wu, Xian ^{[1
]}

机构：

[1] Yunnan Normal Univ, Dept Math, Kunming 650092, Yunnan, Peoples R China

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 248卷

基金：

中国国家自然科学基金;

关键词：

Four-order elliptic equations; Nontrivial solutions; Variational methods; LINEAR SCHRODINGER-EQUATIONS; HIGH-ENERGY SOLUTIONS; SOLITON-SOLUTIONS;

D O I：

10.1016/j.amc.2014.10.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following fourth-order elliptic equation of the form Delta(2)u - Delta u + V(x)u - kappa/2 Delta(u(2))u = h(x, u), x is an element of R-N, where Delta(2) : = Delta(Delta) is the biharmonic operator, kappa >= 0, N <= 6, V is an element of C(R-N, R) and h is an element of C (R-N x R, R). Under appropriate assumptions on V(x) and h(x, u), some existence and multiplicity results for nontrivial solutions are obtained via variational methods. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：593 / 601

页数：9

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