Approximate controllability of semilinear system with state delay using sequence method

The objective of this paper is to present some sufficient conditions for approximate controllability of semilinear system with state delay using sequence method. Instead of a C0-semigroup associated with the mild solution of the system, we use the so-called fundamental solution. Controllability results are obtained by sequential approach and operator semigroup theory. At the end, an example is given to illustrate the theory.