Geodesic
Periodic solutions for systems with nonsmooth and partially coercive potential
Archivum mathematicum, Tome 42 (2006) no. 3, pp. 225-232 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we consider nonlinear periodic systems driven by the one-dimensional $p$-Laplacian and having a nonsmooth locally Lipschitz potential. Using a variational approach based on the nonsmooth Critical Point Theory, we establish the existence of a solution. We also prove a multiplicity result based on a nonsmooth extension of the result of Brezis-Nirenberg (Brezis, H., Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939–963.) due to Kandilakis-Kourogenis-Papageorgiou (Kandilakis, D., Kourogenis, N., Papageorgiou, N., Two nontrivial critical point for nosmooth functional via local linking and applications, J. Global Optim., to appear.).
In this paper we consider nonlinear periodic systems driven by the one-dimensional $p$-Laplacian and having a nonsmooth locally Lipschitz potential. Using a variational approach based on the nonsmooth Critical Point Theory, we establish the existence of a solution. We also prove a multiplicity result based on a nonsmooth extension of the result of Brezis-Nirenberg (Brezis, H., Nirenberg, L., Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939–963.) due to Kandilakis-Kourogenis-Papageorgiou (Kandilakis, D., Kourogenis, N., Papageorgiou, N., Two nontrivial critical point for nosmooth functional via local linking and applications, J. Global Optim., to appear.).
Classification : 34A60, 34B15, 34C25, 47J30, 47N20
Keywords: locally linking Lipschitz function; generalized subdifferential; nonsmooth critical point theory; nonsmooth Palais-Smale condition; $p$-Laplacian; periodic system 
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     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_3_a2/}
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Filippakis, Michael E. Periodic solutions for systems with nonsmooth and partially coercive potential. Archivum mathematicum, Tome 42 (2006) no. 3, pp. 225-232. http://geodesic.mathdoc.fr/item/ARM_2006_42_3_a2/

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