中文摘要：

本文研究了一类非线性二阶三点边值问题的正解的存在性．运用Leray—Schauder不动点定理获得了存在正解的充分条件，改进了文献[1]中的结果．

英文摘要：

In this paper, we investigate the existence of positive solutions for second-order nonlinear three-point boundary value problems. By using Leray-Schauder theorem, some sufficient conditions for the existence of positive solutions are obtained, which improve the results in [1].