Approximate Controllability Of Impulsive Functional Differential System

In this dissertation,we study the approximate controllability for a semilinear impulsive functional equation and a neutral impulsive differential inclusion with nonlocal conditions.Analytic semigroup theory andα-norm arguments are employed to ensure the obtained results be able to be applied to the systems which involves spatial derivatives.Sufficient conditions are established for their approximate controllability.Two examples are also provided to illustrate the applications of the obtained results respectively.This dissertation contains three chapters:In Chapter 1 we introduce some background of Functional differential equations and controllability.In Chapter 2 we study the approximate controllability and complete controllability of a semilinear impulsive functional differential equations.The main methods we adopted are Schauder fixed point theorem and Banach fixed point theorem.In Chapter 3 we investigate the approximate controllability for a neutral impulsive differential inclusion with nonlocal conditions by using the fixed point theorem for condense mappings.