Continuity results for some classes of variational inequalities and applications to time dependent equilibrium problems

We consider a class of monotone variational inequalities in which both the operator and the convex set are parametrized by continuous functions. Under suitable assumptions, we prove the continuity of the solution with respect to the parameter. As an important application, we consider the case of finite dimensional variational inequalities on suitable polyhedra. We demonstrate the applicability of our results to time dependent traffic equilibrium problem.