Asymptotic Behavior of Solutions for a Class of Integrodifferential Equations

The existence of S-asymptotically !-periodic mild solutions for a class of integrodifferential equation is considered. Some sufficient conditions are set up by using properties of S-asymptotically !-periodic function combined with Banach fixed point theorem and strongly continuous family of resolvent operators. S-asymptotically !-periodic system is associated with the optimal periodic control problem for systems governed by ordinary and functional differential equations with the delay type, which appears as dynamical systems model based on approximate periodic motions.