34A60, 47J20, 49J52

In [8] the notion of ``projected differential equation'' has been introduced and the stability of solutions has been studied by means of Stampacchia type variational inequalities. More recently, in [20], Minty variational inequalities have been involved in the study of properties of the trajectories of such a projected differential equation.

We consider classical generalizations of both problems, namely projected differential inclusions and variational inequalities with point to set operators, and we extend results stated in [20] to this setting. Moreover, we also apply the results to describe the convergence of the trajectories of a generalized gradient inclusion method.;