The spectrum and an index formula for the Neumann p-Laplacian and multiple solutions for problems with a crossing nonlinearity

Aizicovici, S; Papageorgiou, NS; Staicu, V

dc.contributor.author	Aizicovici, S	en
dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Staicu, V	en
dc.date.accessioned	2014-03-01T01:32:11Z
dc.date.available	2014-03-01T01:32:11Z
dc.date.issued	2009	en
dc.identifier.issn	1078-0947	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20069
dc.subject	(S)+-operator	en
dc.subject	Crossing nonlinearity	en
dc.subject	Homotopy invariant	en
dc.subject	Index formula	en
dc.subject	Second eigenvalue	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	GLOBAL BIFURCATION	en
dc.subject.other	ELLIPTIC-EQUATIONS	en
dc.subject.other	OPERATORS	en
dc.subject.other	EIGENVALUES	en
dc.title	The spectrum and an index formula for the Neumann p-Laplacian and multiple solutions for problems with a crossing nonlinearity	en
heal.type	journalArticle	en
heal.identifier.primary	10.3934/dcds.2009.25.431	en
heal.identifier.secondary	http://dx.doi.org/10.3934/dcds.2009.25.431	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	In this paper we first conduct a study of the spectrum of the negative p-Laplacian with Neumann boundary conditions. More precisely we investigate the first nonzero eigenvalue. We produce alternative variational characterizations, we examine its dependence on p is an element of (1, infinity) and on the weight function m is an element of L-infinity (Z)(+) and we prove that the isolation of the principal eigenvalue lambda(0) = 0, is uniform for all p in a bounded closed interval. All these results are then used to prove an index formula (jumping theorem) for the d((S)+) -degree map at the first nonzero eigenvalue. Finally the index formula is used to prove a multiplicity result for problems with a multivalued crossing nonlinearity.	en
heal.publisher	AMER INST MATHEMATICAL SCIENCES	en
heal.journalName	Discrete and Continuous Dynamical Systems	en
dc.identifier.doi	10.3934/dcds.2009.25.431	en
dc.identifier.isi	ISI:000267797500002	en
dc.identifier.volume	25	en
dc.identifier.issue	2	en
dc.identifier.spage	431	en
dc.identifier.epage	456	en