Critical points for a class of nondifferentiable functions and applications

Abstract

Some critical point theorems involving functional that are the sum of a locally Lipschitz continuous term and of a convex, proper, besides lower semicontinuous, function are established. A recent existence result of Adly, Buttazzo, and Théra [1, Theorem 2.3] is improved. Applications to elliptic variational-hemivariational inequalities are then examined.