On a min-max principle for non-smooth functions and applications
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.
Existence and classification of critical points for nondifferentiable functions
A general min-max principle established by Ghoussoub is extended to the case of functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. Some topological properties of the min-max-generated critical points in such a framework are then pointed out.