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Multiplicity of nontrivial solutions for elliptic equations with nonsmooth potential and resonance at higher eigenvalues

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Abstract

We consider a semilinear elliptic equation with a nonsmooth, locally Lipschitz potential function (hemivariational inequality). Our hypotheses permit double resonance at infinity and at zero (double-double resonance situation). Our approach is based on the nonsmooth critical point theory for locally Lipschitz functionals and uses an abstract multiplicity result under local linking and an extension of the Castro-Lazer-Thews reduction method to a nonsmooth setting, which we develop here using tools from nonsmooth analysis.

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Authors and Affiliations

  1. Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, 30072, Cracow, Poland

    Leszek Gasiński

  2. Departement de Mathematiques, Université de Perpignan, 66860, Perpignan, France

    Dumitru Motreanu

  3. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

Authors
  1. Leszek Gasiński
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  2. Dumitru Motreanu
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  3. Nikolaos S. Papageorgiou
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Gasiński, L., Motreanu, D. & Papageorgiou, N.S. Multiplicity of nontrivial solutions for elliptic equations with nonsmooth potential and resonance at higher eigenvalues. Proc. Indian Acad. Sci. (Math. Sci.) 116, 233–255 (2006). https://doi.org/10.1007/BF02829789

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  • DOI: https://doi.org/10.1007/BF02829789

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