Approximate Controllability Of Two Kinds Of Partial Functional Differential Systems With Infinite Delay

In this dissertation, by using semigroup theory, the fraction power operator, liner evolution sys-tem theory and fixed point theorem, we establish some sufficient results of approximate controlla-bility for a neutral functional differential system with state-dependent delay and the approximate controllability of a semilinear nonautomous evolution system with state-dependent delay. Two ex-amples are also provided to illustrate the applications of the obtained results respectively.This dissertation contains three chapters:In Chapter1we introduce some background knowl-edge of functional differential equations and the concept of approximate controllability. In Chapter2we investigate the approximate controllability for a neutral functional differential system with state-dependent delay. The main methods we adopted are the fixed point theorem, semigroup and the fraction power operator theory. In Chapter3we study the approximate controllability for the semilinear nonautomous evolution system with state-dependent delay by using Schauder fixed point theorem and the theory of linear evolution system. Since we discuss the problems in an interpolating space, the obtained results can be applied to the partial differential system for which the nonlinear terms involve space variable partial derivatives, and hence improve and extend the existed corre-sponding results of literatures.