A general existence theorem for a multi-valued control problem - Emamizadeh, Behrouz; Liu, Yichen; Zivari-Rezapour, Mohsen (Comptes Rendus. Mathématique)
In this paper, we propose a general existence theorem for a multi-valued control problem. The proof of the theorem is based on a decomposition result of the weak$^\star $ closure of the set containing all the multi-valued controls and the bathtub principle. We also obtain the optimality condition for the optimal control.