JournalszaaVol. 36, No. 2pp. 209–238

Nonlinear Dirichlet Problems with no Growth Restriction on the Reaction

  • Leszek Gasiński

    Jagiellonian University, Kraków, Poland
  • Liliana Klimczak

    Jagiellonian University, Kraków, Poland
  • Nikolaos S. Papageorgiou

    National Technical University of Athens, Greece
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Abstract

We consider nonlinear Dirichlet problems driven by the sum of a pp-Laplacian and a Laplacian and with a Carathéodory reaction which does not satisfy any global growth condition. Instead we assume that it has constant sign zz-dependent zeros. Using variational methods, truncation techniques and Morse theory, we prove multiplicity theorems providing sign information for all the solutions.

Cite this article

Leszek Gasiński, Liliana Klimczak, Nikolaos S. Papageorgiou, Nonlinear Dirichlet Problems with no Growth Restriction on the Reaction. Z. Anal. Anwend. 36 (2017), no. 2, pp. 209–238

DOI 10.4171/ZAA/1586