Nonsmooth Critical Point Theorems Without Compactness

2002/02/12 by Youssef Jabri, Jabri, Youssef
Mathematics · #49J35 #54C60 #58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:49J35 #msc:54C60 #msc:58E05

paper · pdf · doi:10.48550/arxiv.math/0202107

arxiv created 2002/02/12 · arxiv updated 2009/11/30

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

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