Open Access Research

Three solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator

Honghui Yin1,2* and Zuodong Yang1,3

Author Affiliations

1 Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210046, China

2 School of Mathematical Sciences, Huaiyin Normal University, Jiangsu Huaian 223001, China

3 College of Zhongbei, Nanjing Normal University, Jiangsu Nanjing 210046, China

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Boundary Value Problems 2012, 2012:30 doi:10.1186/1687-2770-2012-30

Published: 7 March 2012

Abstract

The existence of at least three weak solutions is established for a class of quasilinear elliptic systems involving the p(x)-Laplace operator with Neumann boundary condition. The technical approach is mainly based on a three critical points theorem due to Ricceri.

MSC: 35D05; 35J60; 58E05.

Keywords:
p(x)-Laplacian; Sobolev space; three critical points theorem