On the existence of extremal periodic solutions for nonlinear parabolic problems with discontinuities

Avgerinos, EP; Papageorgiou, NS

dc.contributor.author	Avgerinos, EP	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:12:09Z
dc.date.available	2014-03-01T01:12:09Z
dc.date.issued	1996	en
dc.identifier.issn	0022-0396	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11975
dc.subject	Boundary Value Problem	en
dc.subject	Parabolic Problem	en
dc.subject	Periodic Solution	en
dc.subject	Second Order	en
dc.subject.classification	Mathematics	en
dc.subject.other	BOUNDARY-VALUE PROBLEMS	en
dc.subject.other	EQUATIONS	en
dc.subject.other	UNIQUENESS	en
dc.title	On the existence of extremal periodic solutions for nonlinear parabolic problems with discontinuities	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jdeq.1996.0176	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jdeq.1996.0176	en
heal.language	English	en
heal.publicationDate	1996	en
heal.abstract	We consider a very general second order nonlinear parabolic boundary value problem. Assuming the existence of an upper solution phi and a lower solution psi satisfying psi less than or equal to phi, we show that the problem has extremal periodic solutions in the order interval K = [psi, phi]. Our proof is based on a general surjectivity result for the sum of two operators of monotone type and on truncation and penalization techniques. In addition we use a result of independent interest which we prove here and which says that the pseudomonotonicity property of A(t,.) can be lifted to its Nemitsky operator. Finally when we impose stronger conditions on the data, we show that the extremal solutions can be obtained with a monotone iterative process. (C) 1996 Academic Press, Inc.	en
heal.publisher	ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS	en
heal.journalName	Journal of Differential Equations	en
dc.identifier.doi	10.1006/jdeq.1996.0176	en
dc.identifier.isi	ISI:A1996VV32000009	en
dc.identifier.volume	132	en
dc.identifier.issue	1	en
dc.identifier.spage	179	en
dc.identifier.epage	201	en