  We consider a nonlinear Neumann elliptic inclusion with a source (reaction
term) consisting of a convex subdifferential plus a multivalued term depending
on the gradient. The convex subdifferential incorporates in our framework
problems with unilateral constraints (variational inequalities). Using
topological methods and the Moreau-Yosida approximations of the subdifferential
term, we establish the existence of a smooth solution.
