On a min-max principle for non-smooth functions and applications

Abstract

Extensions of the seminal Ghoussoub's min-max principle [15] to non-smooth functionals given by a locally Lipschitz continuous term plus a convex, proper, lower semi-continuous function are presented and discussed in this survey paper. The problem of weakening the PalaisSmale compactness condition is also treated. Some abstract consequences as well as applications to elliptic hemivariational or variational-hemivariational inequalities are then pointed out. ©Dynamic Publishers, Inc.