一类半正二阶三点边值问题的向下凸正解

On concave positive solution of two-second three-point boundary value problem

应用锥拉伸与压缩不动点定理,研究一类半正二阶三点边值问题向下凸正解的存在性,引入辅助函数讨论了更一般的奇异二阶三点边值问题,得到向下凸正解的存在性定理。该定理允许非线性项有一个负的下界,推广和改进了一些已知研究结果。

This paper seeks to study the existence of concave positive solution of nonlinear semiposibive second-order three-point boundary value problem by using the theorem on cone expansion and compression and a fixed point theorem on cone. The discussion of a more general problem by using the method of auxiliary function leads to a suggested theorem which ensures that the two-second three-point boundary value problem has one concave positive solution. The theorem allow the nonlinearity to have a minus Lower bound, which helps to generalize and improve many known results.