Nonsmooth Neumann-Type Problems Involving the p-Laplacian |
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Authors: | Alexandru Kristály Dumitru Motreanu |
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Affiliation: | 1. Department of Economics , Babe?-Bolyai University , Cluj-Napoca, Romania;2. Department of Mathematics , Central European University , Budapest, Hungary alexandrukristaly@yahoo.com;4. Département de Mathématiques , Université de Perpignan , Perpignan, France |
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Abstract: | This paper deals with the problem ? Δ p u + α(x)|u| p?2 u = β(x)f(|u|) in Ω, subjected to the zero Neumann boundary condition, where p > 1, Ω ? ? N is bounded with smooth boundary, α, β ? L ∞(Ω), essinfΩβ > 0, and f:[0,+ ∞) → ? is a not necessarily continuous nonlinearity that oscillates either at the origin or at the infinity. By using nonsmooth variational methods, we establish in both cases the existence of infinitely many distinct non-negative solutions of the Neumann problem. In our framework, α:Ω → ? may be a sign-changing or even a nonpositive potential, which is not permitted usually in earlier works. |
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Keywords: | Infinitely many solutions p-Laplacian Neumann problem Nonsmooth potential |
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