Non-linear second-order periodic systems with non-smooth potential

Papageorgiou, EH; Papageorgiou, NS

dc.contributor.author	Papageorgiou, EH	en
dc.contributor.author	Papageorgiou, NS	en
dc.date.accessioned	2014-03-01T02:42:53Z
dc.date.available	2014-03-01T02:42:53Z
dc.date.issued	2004	en
dc.identifier.issn	0253-4142	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/31127
dc.subject	Clarke subdifferential	en
dc.subject	Homoclinic solution	en
dc.subject	Locally Lipschitz function	en
dc.subject	Non-smooth critical point theory	en
dc.subject	Non-smooth Palais-Smale condition	en
dc.subject	Ordinary vector p-Laplacian	en
dc.subject	Poincaré-Wirtinger inequality	en
dc.subject	Problem at resonance	en
dc.subject.classification	Mathematics	en
dc.subject.other	Clarke subdifferential	en
dc.subject.other	Homoclinic solution	en
dc.subject.other	Landesman-Lazer type condition	en
dc.subject.other	Locally Lipschitz function	en
dc.subject.other	Non-smooth critical point theory	en
dc.subject.other	Non-smooth Palais-Smale condition	en
dc.subject.other	Ordinary vectorp-Laplacian	en
dc.subject.other	Problem at resonance	en
dc.subject.other	Boundary value problems	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Integral equations	en
dc.subject.other	Laplace transforms	en
dc.subject.other	Mechanics	en
dc.subject.other	Set theory	en
dc.subject.other	Theorem proving	en
dc.subject.other	Vectors	en
dc.subject.other	Time varying systems	en
dc.title	Non-linear second-order periodic systems with non-smooth potential	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/BF02830004	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF02830004	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	In this paper we study second order non-linear periodic systems driven by the ordinary vector p-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on the potential function. Then we establish the existence of non-trivial homoclinic (to zero) solutions. Our theorem appears to be the first such result (even for smooth problems) for systems monitored by the p-Laplacian. In the last section of the paper we examine the scalar non-linear and semilinear problem. Our approach uses a generalized Landesman-Lazer type condition which generalizes previous ones used in the literature. Also for the semilinear case the problem is at resonance at any eigenvalue.	en
heal.publisher	INDIAN ACADEMY SCIENCES	en
heal.journalName	Proceedings of the Indian Academy of Sciences: Mathematical Sciences	en
dc.identifier.doi	10.1007/BF02830004	en
dc.identifier.isi	ISI:000223918400005	en
dc.identifier.volume	114	en
dc.identifier.issue	3	en
dc.identifier.spage	269	en
dc.identifier.epage	298	en