Existence and multiplicity of solutions for a class of (φ1, φ2)-Laplacian elliptic system in RN via genus theory

被引：13

作者：

Wang, Liben ^{[1
]}

Zhang, Xingyong ^{[1
]}

Fang, Hui ^{[1
]}

机构：

[1] Kunming Univ Sci & Technol, Fac Sci, Dept Math, Kunming 650500, Yunnan, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 01期

基金：

中国国家自然科学基金;

关键词：

(phi(1); phi(2))-Laplacian system; Genus theory; Weak solution; Critical point; POSITIVE SOLUTIONS; EQUATIONS; EIGENVALUES;

D O I：

10.1016/j.camwa.2016.04.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the following nonlinear and non-homogeneous elliptic system involving (phi(1), phi(2))-Laplacian [GRAPHICS] , where he functions V-i(x)(i = 1, 2) are bounded and positive in R-N, the functions phi(i)(t)t(i = 1, 2) are increasing homeomorphisms from R+ onto R+, and the function F is of class C-1 (RN+2, R) and has a sub-linear Orlicz-Sobolev growth. By using the least action principle, we obtain that system has at least one nontrivial solution. When F satisfies an additional symmetric condition, by using the genus theory, we obtain that system has infinitely many solutions. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：110 / 130

页数：21

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