Hartman–Stampacchia results for stably pseudomonotone operators and non-linear hemivariational inequalities

Abstract

We are concerned with two classes of non-standard hemivariational inequalities. In the first case we establish a Hartman–Stampacchia type existence result in the framework of stably pseudomonotone operators. Next, we prove an existence result for a class of non-linear perturbations of canonical hemivariational inequalities. Our analysis includes both the cases of compact sets and of closed convex sets in Banach spaces. Applications to non-coercive hemivariational and variational–hemivariational inequalities illustrate the abstract results of this article.