Neumann problems with double resonance

O'Regan, D; Papageorgiou, NS; Smyrlis, G

dc.contributor.author	O'Regan, D	en
dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Smyrlis, G	en
dc.date.accessioned	2014-03-01T02:11:30Z
dc.date.available	2014-03-01T02:11:30Z
dc.date.issued	2012	en
dc.identifier.issn	12303429	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29925
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-84857851383&partnerID=40&md5=e2c9bd7d0bdf676744210c634a332819	en
dc.subject	C-condition	en
dc.subject	Critical groups	en
dc.subject	Double resonance	en
dc.subject	Homotopy invariance	en
dc.subject	Morse theory	en
dc.subject	Unique continuation property	en
dc.title	Neumann problems with double resonance	en
heal.type	journalArticle	en
heal.publicationDate	2012	en
heal.abstract	We study elliptic Neumann problems in which the reaction term at infinity is resonant with respect to any pair {λ̂m, λ̂m+1} of distinct consecutive eigenvalues. Using variational methods combined with Morse theoretic techniques, we show that when the double resonance occurs in a ""nonprincipal"" spectral interval [λ̂m, λ̂m+1], m ≥ 1, we have at least three nontrivial smooth solutions, two of which have constant sign. If the double resonance occurs in the ""principal"" spectral [λ̂0 = 0, λ̂1], then we show that the problem has at least one nontrivial smooth solution. © 2012 Juliusz Schauder University Centre for Nonlinear Studies.	en
heal.journalName	Topological Methods in Nonlinear Analysis	en
dc.identifier.volume	39	en
dc.identifier.issue	1	en
dc.identifier.spage	151	en
dc.identifier.epage	173	en