Existence Of Boundary Value Problems For A Class Of Impulsive Differential Equations

In this paper,we mainly study the existence problem of solutions for impulsive differential equations under certain boundary conditions.The text is divided into two chapters.The content of the first chapter is the introduction of this article.This chapter will introduce the research background and significance of the impulsive differential equations with boundary conditions,research status of scholars at home and abroad,it also includes related content arrangements,definitions,symbolic explanations and the main work of this article.The main content of the second chapter is to use Leray-Schauder theorem to study the existence of solutions for a class of first order impulsive equation with boundary conditions.u'(t)= Gu(t)+ f(t)a.e.t? J =[0,T],t?tk,u(0)= ?n(T),??[-1,1),?u(tk)= Ik(u(tk),where G:Rn?Rn is continuous,f:[0,T]?Rn,f(·)?L2([0,T]),Ik:Rn?Rn is continuous for k = 1,2,...,p,Rn is n-dimensional Euclidean Space,Ik ? C[Rn,Rn],?x|t=tk=x(tk+)-x(tk-),x(tk-)= x(tk),0<t1<t2<...<tk<...<tp<T.The conclusion of the existence of the solution of the equation is derived,which generalize some previous results.A related example is also given.