Class Of Nonlinear Pulse Equation And Its Applications

Along with the development of modern physics and applied mathematics, many kinds of non-linear problems have emerged, which greatly urged the non-linear functional analysis to be better improved. Non-linear impulsive equation is a more important direction of non-linear functional analysis, because the impul-sive equations have the impulsive phenomenon, the continuous of the solutions is affected by the qualities of impulsive, using the method of nonlinear analysis to study nonlinear impulsive equations is valuable questions. In this paper using fixed point theorem, we discusse several classes of nonlinear impulsive equations and give some sufficient conditions of the existences of solutions. Meanwhile we apply the main results to the existence of solutions for boundary value problems.The thesis is divided into three chapters according to the contents.In Chapter 1, we use Monch fixed point theorem and the method of estimate step by step to study some existence theorems of solutions for the following class of nonlinear impulsive Volterra integral equations where Under loose conditions, we get some existence theorems of so-lutions for the equations. The results we obtained improve and extend known results. Finally, we give some applications to initial value problems for first dif-ferential equations in Banach Spaces to demostrare the main results of this paper.In Chapter 2, the following nonlinear second-order implicit impulsive integro-differential equations in Banach Space is well discussed, where J= [0, a] C R.,0< t1<…< tm< a<+00, f∈C[J xExExExExE, E], x0,y0∈E,λ1≥0,λ2≥0 are constants, where By using the generalized Darbo fixed point theorem and Monch fixed point theorem, we obtain the existence theorems of global solutions for nonlinear second-order implicit impulsive integro-differential equations in Banach spaces.In Chapter 3, we consider a class of second-order implicit impulsive integro-differential equations in Banach Space where are constants, where By using Monch fixed point theorem, we obtain the existence theorems of so-lutions for nonlinear n-order implicit impulsive integro-differential equations in Banach spaces.