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“Two Nontrivial Critical Points for Nonsmooth Functionals via Local Linking and Applications” |
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| Authors: | Dimitrios Kandilakis Nikolaos C Kourogenis Nikolaos S Papageorgiou |
| Institution: | (1) Department of Mathematics, Technical University of Crete, Chania, Crete, 73100, Greece;(2) Department of Applied Mathematics, University of Crete, Herakleion, Crete, 71409, Greece;(3) Department of Mathematics, National Technical University, Zografou Campus, Athens, 15780, Greece |
| Abstract: | In this paper, we extend to nonsmooth locally Lipschitz functionals the multiplicity result of Brezis–Nirenberg (Communication Pure Applied Mathematics and 44 (1991)) based on a local linking condition. Our approach is based on the nonsmooth critical point theory for locally Lipschitz functions which uses the Clarke subdifferential. We present two applications. This first concerns periodic systems driven by the ordinary vector p-Laplacian. The second concerns elliptic equations at resonance driven by the partial p-Laplacian with Dirichlet boundary condition. In both cases the potential function is nonsmooth, locally Lipschitz. |
| Keywords: | Cerami condition Critical point Generalized subdifferential Local linking Locally Lipschitz function Nonsmooth critical point theory Periodic system p-Laplacian Principal eigenvalue Problem at resonance |
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