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

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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 http://hdl.handle.net/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.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

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