Multiple small solutions for p(x)-Schrodinger equations with local sublinear nonlinearities via genus theory

Abstract

In this paper, we deal with the following p(x) - Schrodinger problem: { (-div (vertical bar del u vertical bar(p(x)-2)del u) + V(x) vertical bar u vertical bar(p(x)-2) u = f (x, u) in R-N; u is an element of W-1,W-p(x) (R-N), where the nonlinearity is sublinear. We present the existence of infinitely many solutions for the problem. The main tool used here is a variational method and Krasnoselskii's genus theory combined with the theory of variable exponent Sobolev spaces. We also establish a Bartsch-Wang type compact embedding theorem for the variable exponent spaces.