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locally linking Lipschitz function; generalized subdifferential; nonsmooth critical point theory; nonsmooth Palais-Smale condition; $p$-Laplacian; periodic system
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.).
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