Infinitely many solutions for a differential inclusion problem in ℝ ^N involving p(x)-Laplacian and oscillatory terms

In this paper, we consider the differential inclusion in ℝ ^N involving the p(x)-Laplacian of the type, where p: ℝ ^N → ℝ is Lipschitz continuous function satisfying some given assumptions. The approach used in this paper is the variational method for locally Lipschitz functions. Under suitable oscillatory assumptions on the potential F at zero or at infinity, we show the existence of infinitely many solutions of (P). We also establish a Bartsch-Wang type compact embedding theorem for variable exponent spaces.