On Existence and Multiplicity of Solutions for Elliptic Equations Involving the p-Laplacian

被引：6
|
作者：
Wu, Xian [1 ]
Chen, Jilin [2 ]
机构：
[1] Yunnan Normal Univ, Dept Math, Kunming 650092, Yunnan, Peoples R China
[2] Zhaotong Teachers Coll, Dept Math, Zhaotong 65700, Yunnan, Peoples R China
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2008年 / 15卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Critical point; p-Laplacian; Sobolev's embedding; Dirichlet problem; Neumann problem;
D O I：
10.1007/s00030-008-8017-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian {-Delta(p)(u) = lambda f(x,u), in Omega u = 0, on partial derivative Omega (1.lambda) and {-Delta(p)(u) + a(x)|u|(p-2)u = lambda f(x,u), in Omega partial derivative u/partial derivative n = 0, on partial derivative Omega (2.lambda) are studied and some new multiplicity results of solutions for systems (1.lambda) and (2.lambda) are obtained. Moreover, by using the KKM principle we give also two new existence results of solutions for systems (1.1) and (2.1).
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页码：745 / 755
页数：11
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