The Existence Of Mild Solutions To A Few Class Measure Evolution Equations

As we all know,the theory of measure equation in Banach space is very important on the basis of mathematical equation theory.It is used in many fields of mathematics.Measure differential equations were put forward and studied by Das in the early stage.The nonlocal problem is actually a generalization of the classical Cauchy problem.It was first proposed by Byszewski.Because the nonlocal problem has better application than the Cauchy problem,many authors are interested in it.The existence of abstract differential development systems with nonlocal conditions has been fully studied.This paper is devoted to the problem of "existence of mild solutions".Based on the domestic and foreign research results,we study the existence of mild solutions of semilinear measure evolution equations in Banach spaces under certain conditions.This paper is mainly divided into three chapters.In chapter 2,we discuss a class of semilinear functional measure drive equations with nonlocal conditions.In this chapter,by applying the Schauder fixed point theorem,the existence of mild solutions of semilinear functional measure equations with nonlocal conditions is studied and an example is given.In chapter 3,we discuss a class of semilinear neutral measure equations with nonlocal conditions.In this chapter,the existence of mild solutions for neutral measure equations with nonlocal conditions is discussed by applying the Schauder fixed point theorem and krasnoselskii's fixed point theorem.In chapter 4,we discuss a class of semilinear non-autonomous measure equations with nonlocal conditions.Based on the theory of causal operators,this chapter by applying the Schauder fixed point theorem studies the existence of mild solutions of semilinear non-autono-mous measure equations with nonlocal conditions.