Nonlinear Neumann problems with asymmetric nonsmooth potential

Abstract

In this paper we study a scalar Neumann problem driven by the ordinary p-Lapacian and a nonsmooth potential. The nonlinearity exhibits an asymmetric behavior. Namely growth restriction is imposed in one direction only (either the positive direction or the negative direction). Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz function, we prove the existence of a solution.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.36045/bbms/1126195346

Publication Date

2005

Journal Title

Bulletin of the Belgian Mathematical Society-Simon Stevin

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