Multiple Solutions for Nonhomogeneous Neumann Differential Inclusion Problems by the p(x)-Laplacian - Qing-Mei Zhou (The Scientific World Journal)
A class of nonlinear Neumann problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper is the variational method for locally Lipschitz functions. More precisely, Weierstrass theorem and Mountain Pass theorem are used to prove the existence of at least two nontrivial solutions.