Integral Boundary Value Problem Of Second Order Impulsive Functional Differential Equations

In this paper,we discuss integral boundary value problem of second order impul-sive functional differential equations, and extending the corresponding results in the literatures.In Chapter1, we introduce the research background and positive results of inter-nal and external about second order impulsive functional differential equations, and supplying some fundamental theory and essential knowledge.In Chapter2, we discuss the integral boundary value problem Where J=[0,1], and R+=[0,+∞)；a∈C(J,R), b∈C(J,(-∞,0)),c∈C((0,1),R+), c(t)≠0is allowed to be singular at t=0,1. f∈C(J×R+×…×R+,R+), Tj∈C([0,1],[0,1]), j=1,2,…, n-1; Ii∈C(R+,R+), i=1,2,…,m,g,h∈L1[0,1] is nonnegative; λ is a positive parameter,lct()=tp <t1<t2<…<tm <tm+1=1,△u’|t=tk=u’(tk+)-u’(tk-), where u’(tk-), u’(tk+) respectively denotes the left limit and the right limit of u’(t) at t=tk. Using Krssnosel’skii’s tixed point theorem,we sepa-rately receive a number of ample conditions about the existence of at least one positive solutions or at least two positive solutions of integral boundary value problem(1),and extending the corresponding conclusions in literature [Commun Nonlinear Sci Numer Simulat,2011,16:101-111].In Chapter3, Using Krssnosel’skii’s fixed point theorem, we obtain ample con-dition about the nonexistence of positive solutions for problem (1), and extending the corresponding conclusions in literature [Commun Nonlinear Sci Numer Simulat,201116:101-1111.