Positive Solutions Of Multi-point Boundary Value Problems For Singular Differential Equations

Boundary value problems of differential equations arise in a variety of applied mathematics and physics problems. The problems have been attached much attention by many scholars. In chapter 1 of this thesis, the author explains the present condition of this question.In chapter 2 the author considers the existence of positive solution in the paper for the multi-point boundary value problem of the higher order (k,n-k) differential equation subject to the boundary value conditions respectively, where0<ξ1<ξ2<…<ξm-2< 1, ai∈[0,+∞), and h(x) is allowed to be singular at x= 0 and x= 1.The existence of positive solution is obtained in the paper for the multi-point boundary value problem by means of the extended fixed point theorem concerning cone compression and expansion. The conclusions extend and improve the main results of Zhang Guowei and Sun Jingxian.In chapter 3 the author is concerned with the existence of positive solution for the following second order superlinear singular semipositone differential system subject to the boundary value conditions where f and g:(0, 1)×[0,+∞) x [0,+∞)→[0,+∞) are continuous and allowed to be singular at t=0,1. p and q:(0,1)→(-∞,+∞) are Lebesgue integrable,0<ξ1<ξ2< …<ξm-1 < 1,ai∈(0,+∞).The method is the fixed point theorem concerning cone compression and expansion. The conclusions extend and improve the main results of Liu Lishan.