### Solutions for nonlinear Neumann problems via degree theory for multivalued perturbations of $(S)_+$ maps

#### Abstract

We consider a nonlinear Neumann problem driven by the $p$-Laplacian differential operator and with a nonsmooth potential function (hemivariational inequality). Using a degree-theoretic approach based on the degree map for certain multivalued perturbations of $(S)_+$-operators, we prove the existence of a nontrivial smooth solution.

#### Article information

Source
Adv. Differential Equations, Volume 11, Number 9 (2006), 961-980.

Dates
First available in Project Euclid: 18 December 2012

Agarwal, Ravi P.; Filippakis, Michael E.; O'Regan, Donal; Papageorgiou, Nikolaos S. Solutions for nonlinear Neumann problems via degree theory for multivalued perturbations of $(S)_+$ maps. Adv. Differential Equations 11 (2006), no. 9, 961--980. https://projecteuclid.org/euclid.ade/1355867609