Some remarks on nonsmooth critical point theory

Abstract

A general min---max principle established by Ghoussoub is extended to the case of functionals f which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, when f satisfies a compactness condition weaker than the Palais---Smale one, i.e., the so-called Cerami condition. Moreover, an application to a class of elliptic variational---hemivariational inequalities in the resonant case is presented.