Projected Dynamical Systems and Variational inequalities equivalence results

We present some results of equivalence between projected dynamical systems and variational or quasi-variational inequalities. In particular we prove the result in strictly convex and smooth Banach Spaces, providing also some equivalent formulations in terms of Unilateral differential inclusions. Moreover we obtain for Hilbert spaces, using the Clarke tangent cone, a more general equivalence result with extension to non convex subsets.