Approximate controllability and approximate null controllability of semilinear systems

The approximate controllability and approximate null controllability of controlsystems governed by a class of abstract semilinear integrodifferential equations arediscussed in this paper. Sufficient conditions for approximate controllability andapproximate null controllability are obtained providing the approximatecontrollability and exact null controllability of the corresponding linear systemsrespectively. Finally, some examples are given to illustrate the application of thesufficient conditions.