Nonlinear elliptic differential equations with multivalued nonlinearities

Fiacca, A; Matzakos, N; Papageorgiou, NS; Servadei, R

dc.contributor.author	Fiacca, A	en
dc.contributor.author	Matzakos, N	en
dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Servadei, R	en
dc.date.accessioned	2014-03-01T01:16:48Z
dc.date.available	2014-03-01T01:16:48Z
dc.date.issued	2001	en
dc.identifier.issn	0253-4142	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14226
dc.subject	Coercive operator	en
dc.subject	Critical point	en
dc.subject	Eigenvalue problem	en
dc.subject	Extremal solution	en
dc.subject	Lower solution	en
dc.subject	Nonsmooth Palais-Smale condition	en
dc.subject	Order interval	en
dc.subject	Pseudomonotone operator	en
dc.subject	Truncation function	en
dc.subject	Upper solution	en
dc.subject	Yosida approximation	en
dc.subject.classification	Mathematics	en
dc.subject.other	FUNCTIONALS	en
dc.title	Nonlinear elliptic differential equations with multivalued nonlinearities	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF02829620	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF02829620	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).	en
heal.publisher	INDIAN ACADEMY SCIENCES	en
heal.journalName	Proceedings of the Indian Academy of Sciences: Mathematical Sciences	en
dc.identifier.doi	10.1007/BF02829620	en
dc.identifier.isi	ISI:000172592800009	en
dc.identifier.volume	111	en
dc.identifier.issue	4	en
dc.identifier.spage	489	en
dc.identifier.epage	508	en