Existence and multiplicity of solutions for Neumann problems |
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Authors: | Dumitru Motreanu |
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Institution: | a Université de Perpignan, Département de Mathématiques, 66860 Perpignan, France b National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece |
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Abstract: | In this paper we examine semilinear and nonlinear Neumann problems with a nonsmooth locally Lipschitz potential function. Using variational methods based on the nonsmooth critical point theory, for the semilinear problem we prove a multiplicity result under conditions of double resonance at higher eigenvalues. Our proof involves a nonsmooth extension of the reduction method due to Castro-Lazer-Thews. The nonlinear problem is driven by the p-Laplacian. So first we make some observations about the beginning of the spectrum of (−Δp,W1,p(Z)). Then we prove an existence and multiplicity result. The existence result permits complete double resonance. The multiplicity result specialized in the semilinear case (i.e. p=2) corresponds to the super-sub quadratic situation. |
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Keywords: | 35J20 35J60 35J85 |
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