Pairs of positive solutions for p-Laplacian equations with sublinear and superlinear nonlinearities which do not satisfy the AR-condition

Papageorgiou, NS; Rocha, EM

dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Rocha, EM	en
dc.date.accessioned	2014-03-01T01:31:37Z
dc.date.available	2014-03-01T01:31:37Z
dc.date.issued	2009	en
dc.identifier.issn	0362-546X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19849
dc.subject	(p - 1)-superlinear nonlinearity	en
dc.subject	Ambrosetti-Rabinowitz condition	en
dc.subject	Cerami condition	en
dc.subject	Ekeland variational principle	en
dc.subject	Mountain pass theorem	en
dc.subject	p-Laplacian	en
dc.subject	Positive solutions	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	Equations of state	en
dc.subject.other	Landforms	en
dc.subject.other	Laplace transforms	en
dc.subject.other	Variational techniques	en
dc.subject.other	(p - 1)-superlinear nonlinearity	en
dc.subject.other	Ambrosetti-Rabinowitz condition	en
dc.subject.other	Cerami condition	en
dc.subject.other	Ekeland variational principle	en
dc.subject.other	Mountain pass theorem	en
dc.subject.other	p-Laplacian	en
dc.subject.other	Positive solutions	en
dc.subject.other	Nonlinear equations	en
dc.title	Pairs of positive solutions for p-Laplacian equations with sublinear and superlinear nonlinearities which do not satisfy the AR-condition	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.na.2008.07.042	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.na.2008.07.042	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	We consider a nonlinear Dirichlet problem driven by the p-Laplacian differential. The right-hand-side nonlinearity, exhibits a (p - l)-sublinear term of the form m(z) vertical bar x vertical bar(r-2)x, r < p (concave term), and a Caratheodory term f (z, x) which is (p - 1)-superlinear near +infinity. However, it does not satisfy the usual Ambrosetti-Rabinowitz condition (AR-condition). Instead we employ a more general condition. Using a variational approach based on the critical point theory and the Ekeland variational principle, we show the existence of two nontrivial positive smooth solutions and then the existence of two nontrivial negative smooth solutions. (C) 2008 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.2008.07.042	en
dc.identifier.isi	ISI:000265451800009	en
dc.identifier.volume	70	en
dc.identifier.issue	11	en
dc.identifier.spage	3854	en
dc.identifier.epage	3863	en