Abstract Space Is The Solution Of Ordinary Differential Equations And Their Applications

The paper is divided into four chapters according to contents.The first chapter is a preface.In the second chapter, we shall study the existence and uniqueness of solutions of the nonlinear operator equation u = A(u, u) and give applications to integral equations in Banach spaces.In the third chapter, by establishing a new comparison result, we extend the domainant conditions in the paper[24] and obtain the existence of the following initial value problems for systems of nonlinear second-order integro-differential equations in Banach spaces:The results in this chapter generalize and improve the main results in [24]. In the forth chapter, under further extended conditions, we discuss the existence of solutions of the following initial value problems for systems of nonlinear first-oder impulsive intergro-differential equations in Banachspaces:we weaken some key conditions in [26]. The results in this chapter generalize and improve the main results in [25,26].