Existence and multiplicity of solutions for Neumann problems

Motreanu, D; Papageorgiou, NS

dc.contributor.author	Motreanu, D	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:26:19Z
dc.date.available	2014-03-01T01:26:19Z
dc.date.issued	2007	en
dc.identifier.issn	0022-0396	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18013
dc.subject	Double resonance	en
dc.subject	Eigenvalues and eigenvectors	en
dc.subject	Generalized subdifferential	en
dc.subject	Linking sets	en
dc.subject	Local linking reduction method	en
dc.subject	Neumann problem	en
dc.subject	Nonsmooth critical point theory	en
dc.subject	p-Laplacian	en
dc.subject.classification	Mathematics	en
dc.subject.other	BOUNDARY-VALUE-PROBLEMS	en
dc.subject.other	SEMILINEAR ELLIPTIC PROBLEMS	en
dc.subject.other	DOUBLE-RESONANCE	en
dc.subject.other	VARIATIONAL-METHODS	en
dc.subject.other	CRITICAL-POINTS	en
dc.subject.other	P-LAPLACIAN	en
dc.subject.other	EQUATIONS	en
dc.subject.other	NONLINEARITIES	en
dc.subject.other	REGULARITY	en
dc.subject.other	OPERATORS	en
dc.title	Existence and multiplicity of solutions for Neumann problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jde.2006.09.008	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jde.2006.09.008	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	In this paper we examine semilinear and nonlinear Neumann problems with a nonsmooth locally Lipschitz potential function. Using variational methods based on the nonsmooth critical point theory, for the semilinear problem we prove a multiplicity result under conditions of double resonance at higher eigenvalues. Our proof involves a nonsmooth extension of the reduction method due to Castro-Lazer-Thews. The nonlinear problem is driven by the p-Laplacian. So first we make some observations about the beginning of the spectrum of (-Delta(p), W-1,W-p (Z)). Then we prove an existence and multiplicity result. The existence result permits complete double resonance. The multiplicity result specialized in the semilinear case (i.e. p = 2) corresponds to the super-sub quadratic situation. (c) 2006 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	Journal of Differential Equations	en
dc.identifier.doi	10.1016/j.jde.2006.09.008	en
dc.identifier.isi	ISI:000243310800001	en
dc.identifier.volume	232	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	35	en