Nonsmooth generalized guiding functions for periodic differential inclusions

Filippakis, M; Gasinski, L; Papageorgiou, NS

dc.contributor.author	Filippakis, M	en
dc.contributor.author	Gasinski, L	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T01:24:46Z
dc.date.available	2014-03-01T01:24:46Z
dc.date.issued	2006	en
dc.identifier.issn	1021-9722	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17419
dc.subject	Clarke subdifferential	en
dc.subject	Generalized guiding function	en
dc.subject	Leray-Schauder degree	en
dc.subject	Locally Lipschitz function	en
dc.subject	Nonconvex-valued vector field	en
dc.subject	Periodic solutions	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	TOPOLOGICAL-DEGREE	en
dc.subject.other	EXISTENCE	en
dc.subject.other	EQUATIONS	en
dc.subject.other	R(N)	en
dc.title	Nonsmooth generalized guiding functions for periodic differential inclusions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00030-005-0028-1	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00030-005-0028-1	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	We consider the periodic problem for differential inclusions in ℝN with a nonconvex-valued orientor field F(t, ζ), which is lower semicontinuous in ζ ∈ ℝN. Using the notion of a nonsmooth, locally Lipschitz generalized guiding function, we prove that the inclusion has periodic solutions. We have two such existence theorems. We also study the ""convex"" periodic problem and prove an existence result under upper semicontinuity hypothesis on F(t, •) and using a nonsmooth guiding function. Our work was motivated by the recent paper of Mawhin-Ward [23] and extends the single-valued results of Mawhin [19] and the multivalued results of De Blasi-Górniewicz-Pianigiani [4], where either the guiding function is C 1 or the conditions on F are more restrictive and more difficult to verify. © Birkhäuser Verlag, Basel, 2006.	en
heal.publisher	BIRKHAUSER VERLAG AG	en
heal.journalName	Nonlinear Differential Equations and Applications	en
dc.identifier.doi	10.1007/s00030-005-0028-1	en
dc.identifier.isi	ISI:000236609900003	en
dc.identifier.volume	13	en
dc.identifier.issue	1	en
dc.identifier.spage	43	en
dc.identifier.epage	66	en