Nonsmooth Critical Point Theorems Without Compactness

Mathematics – Functional Analysis

Scientific paper

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Scientific paper

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.

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