中文摘要：

为了将差分方程应用到解无穷区间边值问题,借助于相应线性边值问题Green函数的性质,研究了无穷区间上的二阶三点差分方程边值问题。通过Banach压缩映像原理和LeraySchauder不动点定理获得了该问题正解的存在性和唯一性定理,推广了已有结论。

英文摘要：

In order to apply difference equation in boundary value problem on infinite intervals, with the help of the properties of Green function in linear boundary value problems, the boundary value problem of second-order three-point difference equations on infinite intervals is studied. The theory of existence and uniqueness of positive solutions to this problem is are obtained by Banach ＇ s contraction mapping principle and Leray-Schauder fixed point theorem, which generalizes the known results.