An existence result in Lukes [39] (Theorem 9.2.1) for the system of equations (6)-(9) for bounded coefficients is used to give the first condition. The control set is closed and convex by definition. The right-hand side of the state system (Equations (4.1)-(4.4)) satisfies Condition 3 since the state solutions are a priori bounded. The integrand in the objective functional,