Boundary value problem for multivalued differential equations and controllability (Q1063855)

''Control processes of the type \(\dot x=f(x,t,u)\), \(u\in U(t,x)\) can be deparametrized by writing them in terms of multivalued differential equations. So, under suitable hypotheses, the controllability problem turns out to be equivalent to a two-point boundary value problem for a multi-valued differential equation. In this paper an existence theorem for the latter boundary value problem is sought. The result is achieved by using the fixed-point argument as a crucial tool.'' The assumption of the main result is that the set-valued function F(t,x), where \(\dot x\in F(t,x)\), is compact and upper semicontinuous in the Hausdorff sense.