The Existence Of Solutions For Boundary Value Problems Of Impulsive Differential Equations

The differential equation is an important branch of modern mathematics,which is used to describe the relationship between the derivative of unknown function and variable equation.And it is an effective tool for people to solve various practical problems.At present,there are a lot of theories of differential equations.According to the direction of research,the differential equations can be divided into several categories: integer order differential equations and fractional differential equations;linear differential equation and nonlinear differential equation;resonance and non resonance;impulsive differential equations and differential equations without impulses,and so on.Among them the impulsive differential equations are widely applied to the fields of economics,chemistry,physics,life science,electronics,automatic control,aerospace,engineering and so on.In this thesis,we study the existence of solutions for three kinds of boundary value problems of differential equations with impulses.Firstly,the existence of solutions for two kinds of boundary value problems is studied by the compression mapping principle and Krasnoselskii fixed point theorem.One is the problem of fractional differential equations with countable impulses and integral boundary conditions on the half line,the other is the problem of second order impulsive differential equations with fountional boundary conditions on finite interval.Finally,we study the existence of solutions for the boundary value problems of impulsive differential equations with p-Laplacian at resonance on the half line by the extension continuous theorem of Ge Weigao.