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We consider a nonlinear Neumann elliptic inclusion with a source (reactionterm) consisting of a convex subdifferential plus a multivalued term dependingon the gradient. The convex subdifferential incorporates in our frameworkproblems with unilateral constraints (variational inequalities). Usingtopological methods and the Moreau-Yosida approximations of the subdifferentialterm, we establish the existence of a smooth solution.

Nonlinear elliptic inclusions with unilateral constraint and dependence on the gradient