Existence and Relaxation Results for Nonlinear Second-Order Multivalued Boundary Value Problems in RN

Halidias, N; Papageorgiou, NS

dc.contributor.author	Halidias, N	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:13:44Z
dc.date.available	2014-03-01T01:13:44Z
dc.date.issued	1998	en
dc.identifier.issn	0022-0396	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12697
dc.subject	Maximal monotone map	en
dc.subject	compact operator	en
dc.subject	compact embedding	en
dc.subject	Leary-Schauder alternative theorem	en
dc.subject	continuous selector	en
dc.subject	extremal solution	en
dc.subject	relaxation theorem	en
dc.subject	Aumann's selection theorem	en
dc.subject.classification	Mathematics	en
dc.subject.other	DIFFERENTIAL-INCLUSIONS	en
dc.title	Existence and Relaxation Results for Nonlinear Second-Order Multivalued Boundary Value Problems in RN	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jdeq.1998.3439	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jdeq.1998.3439	en
heal.language	English	en
heal.publicationDate	1998	en
heal.abstract	In this paper we study second order differential inclusions with nonlinear boundary conditions. Our formulation is general and incorporates as special cases well-known problems such as the Dirichlet (Picard), Neumann, and periodic problems. We prove existence theorems under various sets of hypotheses for both the convex and nonconvex problems. Also we show the existence of extremal solutions and that the extremal solutions are dense in the solutions of the convex problem for the W-1,W-2 (T, R-N)-norm (strong relaxation theorem). Finally we examine the Dirichlet problem when the multivalued right-hand side does not depend on the derivative of.x and satisfies a general growth hypothesis and a sign-type condition. For this problem we prove existence results and a relaxation theorem. (C) 1998 Academic Press.	en
heal.publisher	ACADEMIC PRESS INC	en
heal.journalName	Journal of Differential Equations	en
dc.identifier.doi	10.1006/jdeq.1998.3439	en
dc.identifier.isi	ISI:000074828800005	en
dc.identifier.volume	147	en
dc.identifier.issue	1	en
dc.identifier.spage	123	en
dc.identifier.epage	154	en