文献类型：期刊文献

英文题名：On the superlinear problem involving the p(x)-Laplacian

作者：Ji, Chao

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2011

期号：40

起止页码：1

外文期刊名：ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000291252200001)】；

语种：英文

外文关键词：Superlinear problem; p(x)-Laplacian; Variational method; Variable exponent spaces

摘要：This paper deals with the superlinear elliptic problem without Ambrosetti and Rabinowitz type growth condition of the form: {-div(vertical bar del u vertical bar(p(x)-2)del u) = lambda f(x,u) in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N(N >= 2) is a bounded domain with smooth boundary partial derivative Omega, lambda > 0 is a parameter. Existence of nontrivial solution is established for arbitrary lambda > 0. Firstly, by using the mountain pass theorem a nontrivial solution is constructed for almost every parameter lambda > 0. Then, it is considered the continuation of the solutions. Our results are a generalization of Miyagaki and Souto.