Existence of three nontrivial solutions for asymptotically p-linear noncoercive p-Laplacian equations

Papageorgiou, NS; Rocha, EM

dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Rocha, EM	en
dc.date.accessioned	2014-03-01T01:35:40Z
dc.date.available	2014-03-01T01:35:40Z
dc.date.issued	2011	en
dc.identifier.issn	0362-546X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21152
dc.subject	Critical groups	en
dc.subject	Homotopy invariance	en
dc.subject	Morse relation	en
dc.subject	Mountain pass theorem	en
dc.subject	p-Laplacian	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	Critical groups	en
dc.subject.other	Homotopies	en
dc.subject.other	Morse relation	en
dc.subject.other	Mountain pass theorem	en
dc.subject.other	P-Laplacian	en
dc.subject.other	Euler equations	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Laplace transforms	en
dc.title	Existence of three nontrivial solutions for asymptotically p-linear noncoercive p-Laplacian equations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.na.2011.05.014	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.na.2011.05.014	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	We consider a nonlinear elliptic problem driven by the p-Laplacian, where the right hand side nonlinearity exhibits a p-linear behavior near infinity and the Euler functional of the problem need not be coercive and, in fact, can be indefinite. Using a combination of minimax arguments with truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have a constant sign. Our method of proof uses some results on critical groups and the spectrum of the p-Laplacian, due to Perera and Dancer-Perera. (C) 2011 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.2011.05.014	en
dc.identifier.isi	ISI:000292035500008	en
dc.identifier.volume	74	en
dc.identifier.issue	16	en
dc.identifier.spage	5314	en
dc.identifier.epage	5326	en