奇异二阶四点边值问题的正解

Singular Second Order Four-point Boundary Value Problem

研究了如下奇异二阶四点边值问题u″(t)+h(t)f(t,u(t))=0,0<t<1,u(0)=αu(ξ),u(1)=βu(η),其中0<ξ<η<1,0α,β<1,f(t,u)在u=0点具有奇性,h(t)在t=0,1点具有奇性.应用Green函数的性质和存在性原则,得到了正解的存在性.

In this paper, the singular second order four-point boundary value problem {u^n（t）＋h（t）f（t,u（t））=0,0〈t〈1, u（0）=au（ξ）,u（1）=βu（η） is studied, where 0〈ξ〈η〈1,0≤α,β〈1,f（t,u） may be singular at u = 0,h（t） may be singular at t = 0,1. By the use of the property of the corresponding Green＇s function and existence principle, existence of positive solution are acquired.