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

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.

Keywords

• p(x)-Laplacian
• variational method
• radial solution
• Ambrosetti-Rabinowitz condition