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

Authors:	Giuseppina Barletta Nikolaos S Papageorgiou

Institution:	(1) Dipartimento Patrimonio Architettonico e Urbanistico, Facoltà di Architettura, Università di Reggio Calabria, Salita Melissari, 89124 Reggio Calabria, Italy;(2) Departement of Mathematics, National Technical University, Zagrafou Campus, Athens, 15780, Greece

Abstract:	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.

Keywords:	Neumann problem p-Laplacian Degree theory Local minimizer Lagrange multiplier rule Nonsmooth potential
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