Nonsmooth Critical Point Theorems Without Compactness

Youssef Jabri

paper

Nonsmooth Critical Point Theorems Without Compactness

arXiv:math/0202107

Abstract

We establish an abstract critical point theorem for locally Lipschitz functionals that does not require any compactness condition of Palais-Smale type. It generalizes and unifies three other critical point theorems established in [Jabri-Moussaoui] for $C^{1}$ -functionals under slightly stronger assumptions. Our approach uses continuous selections of multivalued mappings.