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Linking-Type Results in Nonsmooth Critical Point Theory and Applications

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Abstract

We generalize to locally Lipschitz functionals defined on a closed ball of a reflexive Banach space with strictly convex dual the critical point theory developed by Schechter for C 1-functionals in Hilbert spaces. Using a constrained deformation theorem which involves the duality mapping various critical point alternatives are obtained. Application to partial differential inclusions governed by the p-Laplacian are also provided in the last section of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Politehnica University of Bucharest, 313 Splaiul Independenţei, 060042, Bucharest, Romania

    Nicuşor Costea

  2. Research Group of the Project PN-II-ID-PCE-2012-4-0021, “Simion Stoilow” Institute of Mathematics of the Romanian Academy, 21 Calea Griviţei, Bucharest, Romania

    Nicuşor Costea

  3. Department of Applied Analysis, Eötvös Loránd University, Pázmány P. Sétány 1/C, 1117, Budapest, Hungary

    Mihály Csirik

  4. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu, 400084, Cluj-Napoca, Romania

    Csaba Varga

  5. Department of Mathematics, University of Pécs, Ifjúság útja 6., 7624, Pécs, Hungary

    Csaba Varga

Authors
  1. Nicuşor Costea
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  2. Mihály Csirik
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  3. Csaba Varga
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Correspondence to Nicuşor Costea.

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Costea, N., Csirik, M. & Varga, C. Linking-Type Results in Nonsmooth Critical Point Theory and Applications. Set-Valued Var. Anal 25, 333–356 (2017). https://doi.org/10.1007/s11228-016-0383-6

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  • DOI: https://doi.org/10.1007/s11228-016-0383-6

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