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

  • Leszek Gasiński
  • Dumitru Motreanu
  • Nikolaos S. Papageorgiou
Regular Articles


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.


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


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Copyright information

© Indian Academy of Sciences 2006

Authors and Affiliations

  • Leszek Gasiński
    • 1
  • Dumitru Motreanu
    • 2
  • Nikolaos S. Papageorgiou
    • 3
  1. 1.Institute of Computer ScienceJagiellonian UniversityCracowPoland
  2. 2.Departement de MathematiquesUniversité de PerpignanPerpignanFrance
  3. 3.Department of MathematicsNational Technical UniversityAthensGreece

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