Multiple solutions to a class of inclusion problems with operator involving p(x)-Laplacian

Abstract

In this paper, we prove the existence of at least two nontrivial solutions for a nonlinear elliptic problem involving p(x)-Laplacian-like operator and nonsmooth potentials. Our approach is variational and it is based on the nonsmooth critical point theory for locally Lipschitz functions.

Keywords

• p(x)-laplacian-like
• differential inclusion
• nonlinear eigenvalue problem
• multiple solutions