Multiple solutions for nonlinear elliptic equations at resonance with a nonsmooth potential

Motreanu, D; Papageorgiou, NS

dc.contributor.author	Motreanu, D	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:21:06Z
dc.date.available	2014-03-01T01:21:06Z
dc.date.issued	2004	en
dc.identifier.issn	0362-546X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16067
dc.subject	Clarke subdifferential	en
dc.subject	Ekeland variational principle	en
dc.subject	Nonlinear regularity	en
dc.subject	Nonsmooth Mountain Pass Theorem	en
dc.subject	Nonsmooth Palais-Smale condition	en
dc.subject	p-Laplacian	en
dc.subject	Principal eigenvalue	en
dc.subject	Resonant problem	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	Differentiation (calculus)	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Functions	en
dc.subject.other	Laplace transforms	en
dc.subject.other	Problem solving	en
dc.subject.other	Theorem proving	en
dc.subject.other	Topology	en
dc.subject.other	Variational techniques	en
dc.subject.other	Clarke subdifferential	en
dc.subject.other	Ekeland variational principle	en
dc.subject.other	Non-linear regularity	en
dc.subject.other	Nonsmooth mountain pass theorem	en
dc.subject.other	Nonsmooth Palais-Smale condition	en
dc.subject.other	P-laplacian	en
dc.subject.other	Principal eigenvalue	en
dc.subject.other	Resonant problem	en
dc.subject.other	Nonlinear equations	en
dc.title	Multiple solutions for nonlinear elliptic equations at resonance with a nonsmooth potential	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.na.2003.11.011	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.na.2003.11.011	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	In this paper, we study a nonlinear elliptic problem at resonance driven by the p-Laplacian and with a nonsmooth potential (hemivariational inequality). Our approach is variational and it is based on the nonsmooth critical point theory for locally Lipschitz functions due to Chang. We prove a theorem guaranteeing the existence of one solution which is smooth and strictly positive. Then by strengthening the assumptions, we establish a multiplicity result providing the existence of at least two distinct solutions. Our hypotheses permit resonance and asymmetric behavior at +infinity and -infinity. As a byproduct of our analysis we obtain an nonlinear and nonsmooth generalization of a result of Brezis-Nirenberg about H-0(1) versus C-0(1) minimizers of a smooth functional. (C) 2003 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Nonlinear Analysis, Theory, Methods and Applications	en
dc.identifier.doi	10.1016/j.na.2003.11.011	en
dc.identifier.isi	ISI:000220261300006	en
dc.identifier.volume	56	en
dc.identifier.issue	8	en
dc.identifier.spage	1211	en
dc.identifier.epage	1234	en