Advertisement

Journal of Global Optimization

, Volume 34, Issue 3, pp 317–337 | Cite as

Nontrivial Solutions for Resonant Hemivariational Inequalities

  • Zdzisław Denkowski
  • Leszek Gasiński
  • Nikolaos S. Papageorgiou
Article

Abstract

We study a resonant semilinear elliptic hemivariational inequality. Under some assumptions of strong resonance on the Clarke subdifferential of the superpotential, and using nonsmooth critical point theory, the existence of a nontrivial solution of the problem is shown.

Keywords

hemivariational inequality strongly resonant problem 

Mathematics Subject Classifications (2000)

35J20 35J85 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bartolo, P., Benci, V., Fortunato, D. 1983Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinityNonlinear Analysis79811012CrossRefGoogle Scholar
  2. 2.
    Solimini, S. 1986On the solvability of some elliptic partial differential equations with the linear part of resonanceJournal of Mathematical Analysis and Applications117138152CrossRefGoogle Scholar
  3. 3.
    Figueiredo, D., Gossez, J.P. 1988Nonresonance below the first eigenvalue for a semilinear elliptic problemMathematische Annalen281889910CrossRefGoogle Scholar
  4. 4.
    Capozzi, A., Lupo, D., Solimini, S. 1989On the existence of a nontrivial solution to nonlinear problems at resonanceNonlinear Analysis13151163CrossRefGoogle Scholar
  5. 5.
    Hirano, N., Nishimura, T. 1993Multiplicity results for semilinear elliptic problems at resonance with jumping nonlinearitiesJournal of Mathematical Analysis and Applications180566586CrossRefGoogle Scholar
  6. 6.
    Iannacci, R., Nkashama, M.N. 1995Nonlinear elliptic partial differential equations at resonance: higher eigenvaluesNonlinear Analysis25455471CrossRefGoogle Scholar
  7. 7.
    Goeleven, D., Motreanu, D., Panagiotopoulos, P.D. 1998Eigenvalue problems for variational-hemivariational inequalities at resonanceNonlinear Analysis33161180CrossRefGoogle Scholar
  8. 8.
    Gasiński, L., Papageorgiou, N.S. 2001Solutions and multiple solutions for quasilinear hemivariational inequalities at resonanceProceedings of the Royal Society Edinburgh Section A, Mathematics131A10911111Google Scholar
  9. 9.
    Clarke, F.H. 1983Optimization and Nonsmooth AnalysisWileyNew YorkGoogle Scholar
  10. 10.
    Hu, S., Papageorgiou, N.S. 2000Handbook of Multivalued Analysis. Volume I: Theory, Volume 419 of Mathematics and its ApplicationsKluwerDordrecht, The NetherlandsGoogle Scholar
  11. 11.
    Chang, K.-C. 1981Variational methods for nondifferentiable functionals and their applications to partial differential equationsJournal of Mathematical Analysis and Applications80102129CrossRefGoogle Scholar
  12. 12.
    Kourogenis, N.C., Papageorgiou, N.S. 2000Nonsmooth critical point theory and nonlinear elliptic equations at resonanceJournal of Australian Mathematical Society & Series A69245271Google Scholar
  13. 13.
    Hu, S., Papageorgiou, N.S. 2000Handbook of Multivalued Analysis. Volume II: Theory, Volume 500 of Mathematics and its ApplicationsKluwerDordrecht, The NetherlandsGoogle Scholar
  14. 14.
    Lebourg, G. 1975Valeur moyenne pour gradient généraliséC. R. Academic Science Paris Séries A–B281795797Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Zdzisław Denkowski
    • 1
  • Leszek Gasiński
    • 1
  • Nikolaos S. Papageorgiou
    • 2
  1. 1.Institute of Computer ScienceJagiellonian UniversityCracowPoland
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

Personalised recommendations