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	2014-03-01T01:33:28Z
dc.date.available	2014-03-01T01:33:28Z
dc.date.issued	2010	en
dc.identifier.issn	0026-9255	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20431
dc.subject	Asymptotically linear equations	en
dc.subject	p-Laplacian	en
dc.subject	Linking sets	en
dc.subject	Critical group	en
dc.subject	Morse relation	en
dc.subject.classification	Mathematics	en
dc.subject.other	BOUNDARY-VALUE-PROBLEMS	en
dc.subject.other	P-LAPLACE EQUATIONS	en
dc.subject.other	NONTRIVIAL SOLUTIONS	en
dc.subject.other	OPERATOR-EQUATIONS	en
dc.subject.other	DOUBLE-RESONANCE	en
dc.subject.other	CRITICAL-POINTS	en
dc.subject.other	NONLINEARITY	en
dc.subject.other	PRINCIPLE	en
dc.subject.other	H-1	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.language	English	en
heal.publicationDate	2010	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 eigenvalue of (-Delta(p), W-0(1,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.	en
heal.publisher	SPRINGER WIEN	en
heal.journalName	MONATSHEFTE FUR MATHEMATIK	en
dc.identifier.doi	10.1007/s00605-009-0094-2	en
dc.identifier.isi	ISI:000271751100005	en
dc.identifier.volume	159	en
dc.identifier.issue	1-2	en
dc.identifier.spage	59	en
dc.identifier.epage	80	en