The Solution Of Abstract Functional Differential Equations With Infinite Delay

In this paper, we firstly consider the existence and uniqueness of generalized solutions for the following functional differential equations with inifinte delay in Banach space where(-A, D(A))is the infinitesimal generator of an analytic semigroups satisfies locally Lipschitz continuous, and A_a is fractional powers of operators A.Next, we discuss the existence and uniqueness of mild solutions for the non-autonomous functional differential equation with infinite delay in Banach space where (-A(t),D)is the infinitesimal generator of a C₀ semigroup for each , and satisfies locally Lipschitz continuous. This paper is compesed of three parts. The first chapter is made up of introduction and preparation which be used in this paper.In the second chapter, we discuss the existence and uniqueness of generalized solution of functional differential equations with infinite delay on the basis of Liang Jin, Xiao Ti–jun ,and other scholars.In the third chapter, under some assumptions in the second chapter, we give the existence and uniqueness of mild solution for non-autonomous functional differential equation with infinite delay.