Journal of Global Optimization

, Volume 37, Issue 2, pp 245–261

Some remarks on nonsmooth critical point theory

Original Paper

DOI: 10.1007/s10898-006-9047-7

Cite this article as:
Livrea, R. & Bisci, G.M. J Glob Optim (2007) 37: 245. doi:10.1007/s10898-006-9047-7

Abstract

A general min–max principle established by Ghoussoub is extended to the case of functionals f which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, when f satisfies a compactness condition weaker than the Palais–Smale one, i.e., the so-called Cerami condition. Moreover, an application to a class of elliptic variational–hemivariational inequalities in the resonant case is presented.

Keywords

Critical points for nonsmooth functions Nonsmooth Cerami condition Elliptic variational–hemivariational inequalities Problem at risonance 

Mathematics Subject Classification (2000)

58E05 49J35 

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Dipartimento di Patrimonio Architettonico e Urbanistico Facoltà di ArchitetturaUniversità di Reggio CalabriaReggio CalabriaItaly

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