Electron. J. Diff. Equ., Vol. 2014 (2014), No. 133, pp. 1-8.

Existence and multiplicity of solutions for p(x)-Laplacian equations in R^N

Bin Ge, Qingmei Zhou

Abstract:
This article concerns the existence and multiplicity of solutions to a class of p(x)-Laplacian equations. We introduce a revised Ambrosetti-Rabinowitz condition, and show that the problem has a nontrivial solution and infinitely many solutions.

Submitted March 4, 2014. Published June 10, 2014.
Math Subject Classifications: 35J60, 35J20, 58E30.
Key Words: p(x)-Laplacian; variational method; radial solution; Ambrosetti-Rabinowitz condition.

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Bin Ge
Department of Applied Mathematics
Harbin Engineering University
Harbin 150001, China
email: gebin04523080261@163.com
Qingmei Zhou
Library, Northeast Forestry University
Harbin 150040, China
email: zhouqingmei2008@163.com

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