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A multiplicity theorem for the Neumann p-Laplacian with an asymmetric nonsmooth potential

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We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequality). By combining variational with degree theoretic techniques, we prove a multiplicity theorem. In the process, we also prove a result of independent interest relating \({W_n^{1,p}}\) and \({C_n^{1}}\) local minimizers, of a nonsmooth locally Lipschitz functional.

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Correspondence to Giuseppina Barletta.

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Barletta, G., Papageorgiou, N.S. A multiplicity theorem for the Neumann p-Laplacian with an asymmetric nonsmooth potential. J Glob Optim 39, 365–392 (2007).

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2000 AMS Subject Classification