一类奇异半正二阶三点边值问题的正解

Positive solutions of singular nonlinear semipositove second-order three-point BVPs

为了使多点边值问题在弹性稳定性理论中得到更广泛的应用,利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 is aimed at realizing a wider use of multi-point boundary problems in the theory of elasticity and stability.The paper introduces the study on the existence of 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,discusses a more general problem by using the method of auxiliary function,and gives a theorem which ensures the two-second three-point boundary value problem has one positive solution.The theorem which allows the nonlinearity to have a minus lower bound serves to generalize and improve many known results.