JournalszaaVol. 29, No. 4pp. 413–428

Existence of Three Nontrivial Smooth Solutions for Nonlinear Resonant Neumann Problems Driven by the <i>p</i>-Laplacian

  • Leszek Gasiński

    Jagiellonian University, Kraków, Poland
  • Nikolaos S. Papageorgiou

    National Technical University of Athens, Greece
Existence of Three Nontrivial Smooth Solutions for Nonlinear Resonant Neumann Problems Driven by the <i>p</i>-Laplacian cover
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Abstract

We consider a nonlinear Neumann elliptic problem driven by the p-Laplacian and with a reaction term which asymptotically at ±∞ exhibits resonance with respect to the principal eigenvalue λ0 = 0. Using variational methods combined with tools from Morse theory, we show that the resonant problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative).

Cite this article

Leszek Gasiński, Nikolaos S. Papageorgiou, Existence of Three Nontrivial Smooth Solutions for Nonlinear Resonant Neumann Problems Driven by the <i>p</i>-Laplacian. Z. Anal. Anwend. 29 (2010), no. 4, pp. 413–428

DOI 10.4171/ZAA/1415