On maximal and minimal solutions for set-valued differential equations with feedback control (Q410236)

Summary: We present the existence of extremal solutions to set-valued differential equations with feedback control \[ D_H X(t) = F(t, X(t),~ H(t, X(t))), ~X(0) = X_0, \text{ for } t \in [0, T], \] \text{where} \(D_H\) is the Hukuhara derivative. We use monotone iterative technique and we will verify that a monotone sequence of approximate solutions converges uniformly to the solution of the problem.