A critical point theorem for a class of non-differentiable functionals with applications

Abstract

This paper presents a multiplicity theorem for a kind of non-smooth functionals. The proof of this theorem relies on a suitable deformation lemma and the perturbation methods. We also apply this result to prove a multiplicity theorem for elliptic variational-hemivariational inequality problems.

Keywords

• critical points
• non-smooth functions
• deformation
• variational-hemivariational inequality
• locally lipschitz continuous