Multiplicity of solutions for a class of resonant p-Laplacian Dirichlet problems

Papageorgiou, EH; Papageorgiou, NS

dc.contributor.author	Papageorgiou, EH	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:31:17Z
dc.date.available	2014-03-01T01:31:17Z
dc.date.issued	2009	en
dc.identifier.issn	0030-8730	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19771
dc.subject	Morse theory	en
dc.subject	Mountain pass theorem	en
dc.subject	p-Laplacian	en
dc.subject	Resonant problem	en
dc.subject	Second deformation theorem	en
dc.subject.classification	Mathematics	en
dc.subject.other	LINEAR ELLIPTIC-EQUATIONS	en
dc.subject.other	SIGN	en
dc.title	Multiplicity of solutions for a class of resonant p-Laplacian Dirichlet problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.2140/pjm.2009.241.309	en
heal.identifier.secondary	http://dx.doi.org/10.2140/pjm.2009.241.309	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	We consider nonlinear Dirichlet problems driven by the p-Laplacian, which are resonant at +infinity with respect to the principal eigenvalue. Using a variational approach based on the critical point theory, we show that the problem has three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative). In the semilinear case, assuming stronger regularity on the nonlinear perturbation f (z, .) and using Morse theory, we show that the problem has at least four nontrivial smooth solutions, two of constant sign.	en
heal.publisher	PACIFIC JOURNAL MATHEMATICS	en
heal.journalName	Pacific Journal of Mathematics	en
dc.identifier.doi	10.2140/pjm.2009.241.309	en
dc.identifier.isi	ISI:000266147800007	en
dc.identifier.volume	241	en
dc.identifier.issue	2	en
dc.identifier.spage	309	en
dc.identifier.epage	328	en