Existence Of Solutions For Multi-Point Boundary Value Problems Of Second-Order Impulsive Differential Equations

Impulsive differential equation was an important branch of differential equations. It not only reflected a kind of instantaneous perturbation phenomenon namely impulsive phenomenon,but also considered the influence of this kind of phenomenon upon the appearance.It had been well used in many science fields,and had been paid attention to extensively and developed deeply in recent years.It was more abundant than the other equations and it could reflect the phenomenon in the objective world more truly,so it was more worth studying.At the same time,Multi-point boundary value problems arised in different fields of applicable mathematics and physics.Because multi-point boundary value problems had wide applied background,they had important value.In recent years,people began to pay attention to the study of multipoint boundary value problems for impulsive differential equations as the development of the theory for impulsive differential equations.Some existence results concerning two-point,three-point or periodic boundary value problems for impulsive differential equations had been obtained,but the existence of solutions of four-point boundary value problems for impulsive differential equations were seldom studied.So it was very meaningful for us to discuss the existence of solutions to multi-point boundary value problems for impulsive differential equations.Lerary-Schauder theory in nonliear analysis was used to solve problems.This paper was made of four parts,we mainly discussed the existence of solutions of multi-point boundary value problems for second-order impulsive differential equations with three different boundary value.In chapter 1,we introduced the history background of multi-point boundary value problems,the current research and our work on this field.In chapter 2,we considered the existence of solutions of multi-point boundary value problems for second-order impulsive differential equations under the condition: x(0)=αx(ξ),x(1)=βx(η).Seven results with respect to the exsitence of solutions were obtained,these include the former.we also gave some examples to demonstrate our conclusion.In chapter 3,we studyed the existence of solutions of multi-point boundary value problems for second-order impulsive differential equations under the condition:x′(0)= αx′(ξ),x(1)=βx(η).Six theorems concerning the exsitence of solutions were obtained, some examples to demonstrate our conclusion were given.In chapter 4,we dicussed the existence of solutions of multi-point boundary value problems fbr second-order impulsive differential equations under the condition:x(0)=αx(ξ),x′(1)=βx′(η).Four theorems about the exsitence of solutions were obtained, some examples to demonstrate our conclusion were given.