Approximate Controllability Of Semilinear Neutral Evolution Systems With Delay

This dissertation considers the approximate controllability for a class of neutral control systems governed by semilinear neutral delayed differential equations. Sufficient conditions for approximate controllability are established by constructing fundamental solutions lia Laplace transform and us-ing resolvent operator condition, Banach contraction mapping principle and techniques on fractional power operators. The obtained results improve some existing analogous ones on this topic to some extent. An example is presented finally to illustrate the applications of the obtained results.This dissertation contains5Sections:In Section1we introduce some background knowledge and research process of functional differential equations and the concept of approximate control-lability. In Section2we introduces the preliminary knowledge about Co-semigroup and fractional power operators. In Section3we construct the fundamental solutions and represent the mild solu-tions of neutral systems by the fundamental solutions. In Section4we investigate the approximate controllability of semilinear neutral evolution systems with delay by using resolvent operator con-dition, Banach contraction mapping principle and techniques on fractional power operators. In Section5we present an example to illustrate the applications of the obtained results. Since we discuss the problems in an interpolating space, the obtained results can be applied to the partial dif-ferential system for which the nonlinear terms involve space variable partial derivatives, and hence improve and extend the existed corresponding results of literatures.