Existence and multiplicity of solutions for asymptotically linear, noncoercive elliptic equations

Motreanu, D; Motreanu, VV; Papageorgiou, NS

dc.contributor.author	Motreanu, D	en
dc.contributor.author	Motreanu, VV	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:58:40Z
dc.date.available	2014-03-01T01:58:40Z
dc.date.issued	2009	en
dc.identifier.issn	00269255	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/28701
dc.subject	Asymptotically linear equations	en
dc.subject	Critical group	en
dc.subject	Linking sets	en
dc.subject	Morse relation	en
dc.subject	p-Laplacian	en
dc.title	Existence and multiplicity of solutions for asymptotically linear, noncoercive elliptic equations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00605-009-0094-2	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00605-009-0094-2	en
heal.publicationDate	2009	en
heal.abstract	First we prove the existence of a nontrivial smooth solution for a p-Laplacian equation with a (p - 1)-linear nonlinearity and a noncoercive Euler functional, under hypotheses including resonant problems with respect to the principal eigen-value of (-Δp, W01,p(Z)). Then, for the semilinear problem (i.e., p = 2), assuming nonuniform nonresonance at infinity and zero, we prove a multiplicity theorem which provides the existence of at least three nontrivial solutions, two being of opposite constant sign. Our approach combines minimax techniques with Morse theory and truncation arguments. © Springer-Verlag 2009.	en
heal.journalName	Monatshefte fur Mathematik	en
dc.identifier.doi	10.1007/s00605-009-0094-2	en
dc.identifier.volume	159	en
dc.identifier.issue	1	en
dc.identifier.spage	59	en
dc.identifier.epage	80	en