带参数的奇异三阶三点边值问题的正解

Positive Solutions to the Problem of Singular Third-order Three-point Boundary Value with a Parameter

本文讨论下述带参数的奇异三阶三点边值问题■其中γ>0是参数且a(t)在t=0和t=1处具有奇性,当f和a满足适当条件时,对一定取值范围内的γ,获得了上述边值问题正解的存在性与不存在性.所用主要工具是Guo-Krasnoselskii不动点定理.

The problem discussed in this paper is singular third-order three-point boundary value with a parameter. It is described as follows：{u″＋λa（t）f（u（t））=0,t∈（0,1）,u（0）-au′（0）=u′（P）=βu′（1）＋λu″（1）=0,where a （t） will be si and the value of A is ngular when t=0 and t=1, and A （λ〉0）is a parameter. Whenfand a satisfy appropriate conditions, limited in certain range （e.g.λ〉0）, we can determine the existence or non-existence of positive solutions to the above problem. The main way used in this paper is the Guo-Krasnoselskii fixed point theorem.