Approximate controllability of a delayed semilinear control system with growing nonlinear term

This paper deals with the approximate controllability of a semilinear control system with delay, where the nonlinear term satisfies the linear growth condition. Sufficient conditions for the approximate controllability of a semilinear control system have been established by assuming that the corresponding linear control system with delay is approximately controllable. To prove our results, the Schauder fixed point theorem is applied and instead of a Co-semigroup associated with the mild solution of the system we use the so-called fundamental solution.