Nonsmooth Critical Point Theorems Without Compactness

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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 C¹-functionals under slightly stronger assumptions. Our approach uses continuous selections of multivalued mappings.