Infinitely many solutions for a class of stationary Schrödinger equations with non-standard growth

Abstract

In this paper, we study the existence of infinitely many solutions for a class of stationary Schrödinger type equations in involving the p(x)-Laplacian. The non-linearity is superlinear but does not satisfy the Ambrosetti-Rabinowitz type condition. The main arguments are based on the geometry supplied by Fountain Theorem. We also establish a Bartsch type compact embedding theorem for variable exponent spaces.