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

Abstract

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.

Keywords

• Locally Lipschitz function
• generalized subdifferential
• second deformation theorem
• Palais-Smale condition