Existence Of Solutions For Impulsive Differential Equations With Integral Boundary Values

Nonlinear functional analysis is a research subject in applied mathematics that has both profound theory and widespread application. It takes the nonlinear problems ap-pearing in mathematics and natural sciences as background to establish some general theories and methods to handle nonlinear problems.The thesis is divided into two chapters, The chapter 1, we study the following frac-tional impulsive differential equations with integral boundary condition:By using the Banach contraction principle,Krasnoselskii's fixed point theorem.we gain the existence and uniqueness of solutions.Compared with the document [10],the equation (1.1.1) not only adds a integral boundary value conditions, but also gives the value of u(t) in t=1,at the same time the function of the equation [1.1.1] replace the f(t,u(t)) with ?u(t)+f(t,u(t),(Ku)(t)(Hu)(t)),Where t € J,are two integral operators with integral kernel.The chapter 2, we study the following fractional impulsive differential equations with integral boundary conditions:By using the Banach contraction principle,Krasnoselskii's fixed point theorem,Banach fixed point theorem we gain the existence and uniqueness of solutions.Compared with the problem of the document [22],the equation (2.1.1) not only contains the document [22], but also adds the two nonlinear integral term to the boundary value.At the same time on the basis of the document [22],by using the Banach contraction mapping theory we receive the further evidence that the uniqueness of the equations.