Boundary value problem for multivalued differential equations and controllability

Control process of the type x = f(t, x, u), u?U(t, x), can be deparametrized by writing them in terms of multivalued differential equations of the form x?F(t, x) = {f(t, x, u): u?U(t, x)}. So, under suitable hypotheses, the controllability problem turns out to be equivalent to a two-point boundary value problem for a multivalued differential equation. In this paper an existence theorem is sought for the latter boundary value problem. The result is achieved by using the fixed point argument as a crucial tool.