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

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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 http://hdl.handle.net/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


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