A controllability technique for nonlinear systems

R denotes a set valued mapping from I x En into the set of nonempty closed subsets of Euclidean n-dimensional space En which is upper semicontinuous with respect to set inclusion. Tarnove [l] used a fixed point theorem to obtain sufficient conditions for A-controllability of the nonlinear system k =f(t, X, u), A a nonempty bounded closed convex set of continuous functions. (A system is said to be A-controllable if there exists a solution of the system belonging to A.) Although Tarnove did not consider generalized differential equations in the notation of this paper, he proved that the system f ==f(t, x, u) is B,-controllable if Q(y) # $4 for all y E B, ,