Well-posedness and approximate controllability for some integrodifferential evolution systems with multi-valued nonlocal conditions

In this work, we study the existence of the mild solutions and the approximate controllability of some integrodifferential evolution systems with multi-valued nonlocal conditions. We use the resolvent operators theory to obtain sufficient conditions for the existence and controllability results. We present a general Kalman's controllability criterion to study the approximate controllability in linear cases. Consequently, we prove the approximate controllability in the nonlinear cases. Some examples are given to illustrate our main results.