Some Results Of Boundary Value Problems Of Implusive Differential Equations

In biotechnology,economics and so on,The theory of implusive differential eqa-tions is of great value both in theory and application. Subsequently,many research workers continued to study and develop the theory of singular boundary value prob-lems with impulse,see[10],[11]. Along with the problem study thoroughly,most methods they applied are the method of upper and lower solutions and cone the-ory,this paper makes use of three solutions theorem,sadvoskii fixed point theorem, Monch fixed point theorem,cone compression and expansion fixed point theorem. Thus we get the existence of positive solutions,the dissertation contains four chap-ters.Chapter 1 investigates the existence of positive solutions of second order sin-gular boundary value problem of impulsive differential equations where a(t)is singularity at t=0. t=1.In this chapter,by using a new three solutions theorem,see[3]we obtain three positive solutions.In chapter 2, we consider the existence of positive solutions of singular bound- ary value problem of impulsive differential equations Where f(t, x(t), (Tx)(t), (Sx)(t))is singularity at t=θ,t= 1,x=θ,Ik,Hkis singu-larity at x=θ.By constructing a special cone and using the Sadovskii fixed point theorem, we get the existence of positive solutions and work out an example to indicate the application.In chapter 3, we study the second order singular value problem of impulsive differential equations in infinite space Where f(t, x(t), x'(t))is singularity at x=θ, x'=θ,Ik, Hk is singularity at x=θ.we mainly use Monch fixed point theorem and get the existence of positive solutions in abstract space.In chapter 4, investigates the existence of positive solutions of 4-order SBVP Where f(t,u(t),u'(t)) is singularity at u=0, t=0,t=1,By using cone compres-sion and expansion fixed point theorem,we the existence of positive solutions.