Existence theorem for a class of generalized quasi-variational inequalities

In this paper we consider a class of generalized quasi-variational inequalities. The variational problem is studied in the convex set X × Y , with Y bounded and X unbounded. In the latter settings, we investigate about the solvability of the problem. In particular, by using the perturbation theory, we give an existence result of the solution without requesting any coercivity hypothesis on the operator. Finally, we give an application to the obtained theoretical results in terms of an economic equilibrium problem.