Existence results of infinitely many solutions for p(x)-Laplacian elliptic Dirichlet problems

Abstract

The existence of infinitely many solutions for a Dirichlet problem involving the p(x)-Laplacian is established. In our main result, under an appropriate oscillating behaviour of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Further, some applications and examples are pointed out. In particular, an existence result of infinitely many solutions for a two-point boundary value problem involving the variable exponent is presented. The approach is based on variational methods.