On the multiplicity of solutions for non-linear periodic problems with the non-linearity crossing several eigenvalues

Kyritsi, ST; Papageorgiou, NS

dc.contributor.author	Kyritsi, ST	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:34:01Z
dc.date.available	2014-03-01T01:34:01Z
dc.date.issued	2010	en
dc.identifier.issn	0017-0895	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20652
dc.subject	Eigenvalues	en
dc.subject	Multiplicity of Solutions	en
dc.subject.classification	Mathematics	en
dc.subject.other	P-LAPLACIAN	en
dc.subject.other	NONTRIVIAL SOLUTIONS	en
dc.subject.other	EQUATIONS	en
dc.subject.other	FUNCTIONALS	en
dc.subject.other	EXISTENCE	en
dc.title	On the multiplicity of solutions for non-linear periodic problems with the non-linearity crossing several eigenvalues	en
heal.type	journalArticle	en
heal.identifier.primary	10.1017/S0017089509990346	en
heal.identifier.secondary	http://dx.doi.org/10.1017/S0017089509990346	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	In this paper we consider a non-linear periodic problem driven by the scalar p-Laplacian and with a non-smooth potential. We assume that the multi-valued right-hand-side non-linearity exhibits an asymmetric behaviour at ±∞ and crosses a finite number of eigenvalues as we move from -∞ to +∞. Using a variational approach based on the non-smooth critical-point theory, we show that the problem has at least two non-trivial solutions, one of which has constant sign. For the semi-linear (p = 2), smooth problem, using Morse theory, we show that the problem has at least three non-trivial solutions, again one with constant sign. © Glasgow Mathematical Journal Trust 2009.	en
heal.publisher	CAMBRIDGE UNIV PRESS	en
heal.journalName	Glasgow Mathematical Journal	en
dc.identifier.doi	10.1017/S0017089509990346	en
dc.identifier.isi	ISI:000277348200006	en
dc.identifier.volume	52	en
dc.identifier.issue	2	en
dc.identifier.spage	271	en
dc.identifier.epage	302	en