2007 Conference on Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems. Electron. J. Diff. Eqns., Conference 18 (2010), pp. 57-66.

Existence and multiplicity of solutions for the noncoercive Neumann p-Laplacian

Nikolaos S. Papageorgiou, Eugenio M. Rocha

We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator with a nonsmooth potential (hemivariational inequality). Using variational techniques based on the smooth critical point theory and the second deformation theorem, we prove an existence theorem and a multiplicity theorem, under hypothesis that in general do not imply the coercivity of the Euler functional.

Published July 10, 2010.
Math Subject Classifications: 35J25, 35J80.
Key Words: Locally Lipschitz function; generalized subdifferential; second deformation theorem; Palais-Smale condition.

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  Nikolaos S. Papageorgiou
Department of Mathematics, National Technical University
Zografou Campus, Athens 15780, Greece
email: npapg@math.ntua.gr
Eugenio M. Rocha
Department of Mathematics, Campus de Santiago
University of Aveiro, 3810-193 Aveiro, Portugal
email: eugenio@ua.pt

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