Existence and Relaxation Theorems for Nonlinear Multivalued Boundary Value Problems

Avgerinos, EP; Papageorgiou, NS

dc.contributor.author	Avgerinos, EP	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:14:35Z
dc.date.available	2014-03-01T01:14:35Z
dc.date.issued	1999	en
dc.identifier.issn	0095-4616	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13164
dc.subject	Coercive operator	en
dc.subject	Compact embedding	en
dc.subject	Continuous selection	en
dc.subject	Extremal solution	en
dc.subject	Integration by parts	en
dc.subject	Leray-Schauder principle	en
dc.subject	Maximal monotone operator	en
dc.subject	Strong relaxation	en
dc.subject	Weak norm	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Integration	en
dc.subject.other	Mathematical operators	en
dc.subject.other	Theorem proving	en
dc.subject.other	Leray-Schauder principle	en
dc.subject.other	Maximal monotone operator	en
dc.subject.other	Relaxation theorem	en
dc.subject.other	Boundary value problems	en
dc.title	Existence and Relaxation Theorems for Nonlinear Multivalued Boundary Value Problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s002459900106	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s002459900106	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	In this paper we consider a general nonlinear boundary value problem for second-order differential inclusions. We prove two existence theorems, one for the ""convex"" problem and the other for the ""nonconvex"" problem. Then we show that the solution set of the latter is dense in the C1(T, RN)-norm to the solution set of the former (relaxation theorem). Subsequently for a Dirichlet boundary value problem we prove the existence of extremal solutions and we show that they are dense in the solutions of the convexified problem for the C1(T, RN)-norm. Our tools come from multivalued analysis and the theory of monotone operators and our proofs are based on the Leray-Schauder principle.	en
heal.publisher	SPRINGER VERLAG	en
heal.journalName	Applied Mathematics and Optimization	en
dc.identifier.doi	10.1007/s002459900106	en
dc.identifier.isi	ISI:000077519400005	en
dc.identifier.volume	39	en
dc.identifier.issue	2	en
dc.identifier.spage	257	en
dc.identifier.epage	279	en