带参数的奇异三阶三点边值问题的正解

摘要

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.%本文讨论下述带参数的奇异三阶三点边值问题{u″＋λa（t）f（u（t））=0,t∈（0,1）,u（0）-au′（0）=u′（P）=βu′（1）＋λu″（1）=0,其中γ〉0是参数且a（t）在t=0和t=1处具有奇性，当f和α满足适当条件时，对一定取值范围内的y，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．