Non-linear second-order periodic systems with non-smooth potential
| dc.creator | Papageorgiou, Evgenia H | |
| dc.creator | Papageorgiou, Nikolaos S | |
| dc.date | 2005-03-05 | |
| dc.date.accessioned | 2026-07-07T05:17:40Z | |
| dc.date.available | 2026-07-07T05:17:40Z | |
| dc.description | 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 \hbox{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. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503087 | |
| dc.identifier | http://arxiv.org/abs/math/0503087 | |
| dc.identifier | Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 3, August 2004, pp. 269-298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74392 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 34B15; 34C25; 34C37; 34A60 | |
| dc.title | Non-linear second-order periodic systems with non-smooth potential | |
| dc.type | text |