Existence and Approximate Controllability of Semilinear Measure Driven Systems with Nonlocal Conditions

The purpose of this paper is to study the existence of mild solutions and approximate controllability formeasure driven evolution systemwith nonlocal conditions. First, we obtain the existence of mild solutions and approximate controllability for the concerned problem by constructing newGreen’s function and control function involving Gramian controllability operator. This research relies on Schauder’s fixed point theorem and the theory of operator semigroup. At the end, two examples are also given to illustrate the feasibility of our theoretical results.