Displaying similar documents to “Coercivity of set-valued mappings on metric spaces.”

A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

Corvellec, J. (1996)

Serdica Mathematical Journal

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The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1]...

Discontinuous quasilinear elliptic problems at resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1998)

Colloquium Mathematicae

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In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.