Approximate Controllability for Nonautonomous Integrodifferential Equations With State-Dependent Delay

We study the existence of mild solutions and the approximate controllability for nonautonomous integro-differential equations with state-dependent delay. We assume the approximate controllability of the linear part, and then we use resolvent operator theory to prove the approximate controllability of the nonlinear case. An example of the one-dimensional heat equation with memory is given to illustrate the basic idea our results.