A multiplicity theorem for problems with the p-Laplacian

Papageorgiou, EH; Papageorgiou, NS

dc.contributor.author	Papageorgiou, EH	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:25:43Z
dc.date.available	2014-03-01T01:25:43Z
dc.date.issued	2007	en
dc.identifier.issn	0022-1236	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17739
dc.subject	Eigenvalues of the p-Laplacian	en
dc.subject	Multiple nontrivial solutions	en
dc.subject	Second deformation theorem	en
dc.subject	Superlinear nonlinearity	en
dc.subject	Upper and lower solutions	en
dc.subject.classification	Mathematics	en
dc.subject.other	QUASILINEAR ELLIPTIC-EQUATIONS	en
dc.subject.other	SOBOLEV	en
dc.title	A multiplicity theorem for problems with the p-Laplacian	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jfa.2006.11.015	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jfa.2006.11.015	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	We consider a nonlinear elliptic problem driven by the p-Laplacian, with a parameter, lambda is an element of R and a non-linearity exhibiting a superlinear behavior both at zero and at infinity. We show that if the parameter; is bigger than lambda(2) = the second eigenvalue of (-Delta(p), W-0(1.p) (Z)), then the problem has at least three nontrivial solutions. Our approach combines the method of upper-lower solutions with variational techniques involving the Second Deformation Theorem. The multiplicity result that we prove extends an earlier semilinear (i.e. p = 2) result due to Struwe [M. Struwe, Variational Methods, Springer-Verlag, Berlin, 1990]. (c) 2006 Elsevier Inc. All rights reserved.	en
heal.publisher	ACADEMIC PRESS INC ELSEVIER SCIENCE	en
heal.journalName	Journal of Functional Analysis	en
dc.identifier.doi	10.1016/j.jfa.2006.11.015	en
dc.identifier.isi	ISI:000244802600003	en
dc.identifier.volume	244	en
dc.identifier.issue	1	en
dc.identifier.spage	63	en
dc.identifier.epage	77	en