Multiple solutions of constant sign for nonlinear nonsmooth eigenvalue problems near resonance

Kyritsi, STh; Papageorgiou, NS

dc.contributor.author	Kyritsi, STh	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	0944-2669	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16068
dc.subject	Critical Point	en
dc.subject	Eigenvalue Problem	en
dc.subject	locally lipschitz function	en
dc.subject	Multiple Solution	en
dc.subject	nonsmooth critical point theory	en
dc.subject	Principal Eigenvalue	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	ELLIPTIC-EQUATIONS	en
dc.subject.other	DIRICHLET PROBLEMS	en
dc.title	Multiple solutions of constant sign for nonlinear nonsmooth eigenvalue problems near resonance	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00526-003-0223-z	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00526-003-0223-z	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	In this paper we study a class of nonlinear elliptic eigenvalue problems driven by the p-Laplacian and having a nonsmooth locally Lipschitz potential. We show that as the parameter lambda approaches lambda(1) (= the principal eigenvalue of (-Deltap, W-0(1,p) (Z))) from the right, the problem has three nontrivial solutions of constant sign. Our approach is variational based on the nonsmooth critical point theory for locally Lipschitz functions. In the process of the proof we also establish a generalization of a recent result of Brezis and Nirenberg for C-0(1) versus W-0(1,p) minimizers of a locally Lipschitz functional. In addition we prove a result of independent interest on the existence of an additional critical point in the presence of a local minimizer of constant sign. Finally by restricting further the asymptotic behavior of the potential at infinity, we show that for all >> lambda(1) the problem has two solutions one strictly positive and the other strictly negative.	en
heal.publisher	SPRINGER-VERLAG	en
heal.journalName	Calculus of Variations and Partial Differential Equations	en
dc.identifier.doi	10.1007/s00526-003-0223-z	en
dc.identifier.isi	ISI:000220497500001	en
dc.identifier.volume	20	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	24	en