Time-varying integro-differential inclusions with Clarke sub-differential and non-local initial conditions: existence and approximate controllability (Q827657)

In this paper the authors have studied a time-varying semi-linear integrodifferential inclusion with Clarke sub-differential and a non-local initial condition. By a suitable Green function combined with a resolvent operator, they formulated its mild solutions and shown that it admits at least one mild solution in a well-defined ball with large radius. A characterization of the approximate controllability for its related linear system in Green function terms is derived, and then established a sufficient condition for the approximate controllability of the time-varying semi-linear integro-differential inclusion. Further finite approximate controllability of the time-varying semi-linear integro-differential inclusion is considered via variational method. An example is provided to illustrate the theory.