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Zeitschrift für Analysis und ihre Anwendungen


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Volume 29, Issue 4, 2010, pp. 413–428
DOI: 10.4171/ZAA/1415

Published online: 2010-10-02

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

Leszek Gasiński[1] and Nikolaos S. Papageorgiou[2]

(1) Jagiellonian University, Kraków, Poland
(2) National Technical University of Athens, Greece

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).

Keywords: p-Laplacian, resonance, critical groups, local minimizers, contractible sets

Gasiński Leszek, Papageorgiou Nikolaos: Existence of Three Nontrivial Smooth Solutions for Nonlinear Resonant Neumann Problems Driven by the p-Laplacian. Z. Anal. Anwend. 29 (2010), 413-428. doi: 10.4171/ZAA/1415