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    • Keywords


      Double resonance; reduction method; eigenvalue; hemivariational inequality; locally Lipschitz function; Clarke subdifferential; critical point; local linking; nonsmooth Cerami condition

    • 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.

    • Author Affiliations


      Leszek Gasiński1 Dumitru Motreanu2 Nikolaos S Papageorgiou3

      1. Institute of Computer Science, Jagiellonian University, ul. Nawojki 11, Cracow - 30072, Poland
      2. Departement de Mathematiques, Université de Perpignan, Perpignan - 66860, France
      3. Department of Mathematics, National Technical University, Zografou Campus, Athens - 15780, Greece
    • Dates

  • Proceedings – Mathematical Sciences | News

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