Nonlinear Neumann problems with asymmetric nonsmooth potential
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.
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Nonlinear Neumann problems with asymmetric nonsmooth potential." Bulletin of the Belgian Mathematical Society-Simon Stevin 12, no. 3 (2005): 417-433.