Resonant equations with the Neumann p-Laplacian plus an indefinite potential |
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Authors: | Leszek Gasiński Nikolaos S Papageorgiou |
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Institution: | 1. Jagiellonian University, Faculty of Mathematics and Computer Science, ul. ?ojasiewicza 6, 30-348 Kraków, Poland;2. National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece |
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Abstract: | We consider a nonlinear Neumann problem driven by the p -Laplacian plus an indefinite potential and a Carathéodory reaction which at ±∞ is resonant with respect to any nonprincipal variational eigenvalue of the differential operator. Using critical point theory and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign. In the process we prove some results of independent interest concerning the unique continuation property of eigenfunctions and the critical groups at infinity of a C1-functionals. |
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Keywords: | Indefinite potential Local regularity Critical groups Homotopy equivalent sets Solutions of constant sign Nonlinear maximum principle |
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