Properties of the solution set of nonlinear evolution inclusions

Papageorgiou, NS; Shahzad, N

dc.contributor.author	Papageorgiou, NS	en
dc.contributor.author	Shahzad, N	en
dc.date.accessioned	2014-03-01T01:13:17Z
dc.date.available	2014-03-01T01:13:17Z
dc.date.issued	1997	en
dc.identifier.issn	0095-4616	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12409
dc.subject	Compact embedding	en
dc.subject	Connected set	en
dc.subject	Evolution inclusion	en
dc.subject	Evolution triple	en
dc.subject	Invariant set	en
dc.subject	Parabolic problem	en
dc.subject	Path-connected set	en
dc.subject	Periodic solution	en
dc.subject	Rδ-set	en
dc.subject	Tangent cone	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Functions	en
dc.subject.other	Invariance	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Problem solving	en
dc.subject.other	Gelfand triple of spaces	en
dc.subject.other	Nonlinear evolution inclusions	en
dc.subject.other	Nonlinear equations	en
dc.title	Properties of the solution set of nonlinear evolution inclusions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF02683335	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF02683335	en
heal.language	English	en
heal.publicationDate	1997	en
heal.abstract	In this paper we examine nonlinear, nonautonomous evolution inclusions defined on a Gelfand triple of spaces. First we show that the problem with a convex-valued, h*-usc in x orientor field F(t, x) has a solution set which is an Rδ-set in C (T, H). Then for the problem with a nonconvex-valued F (t, x) which is h-Lipschitz in x, we show that the solution set is path-connected in C (T, H). Subsequently we prove a strong invariance result and a continuity result for the solution multifunction. Combining these two results we establish the existence of periodic solutions. Some examples of parabolic partial differential equations with multivalued terms are also included. © 1997 Springer-Verlag New York Inc.	en
heal.publisher	SPRINGER VERLAG	en
heal.journalName	Applied Mathematics and Optimization	en
dc.identifier.doi	10.1007/BF02683335	en
dc.identifier.isi	ISI:A1997WX23300001	en
dc.identifier.volume	36	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	20	en