二阶微分方程的三点边值问题

Three-Point Boundary Value Problem for Second Order Differential Equations

在已有的二阶微分方程的两点边值问题的微分不等式理论的基础上,进一步研究二阶微分方程的三点边值问题的解的存在性。不仅提出了该类三点边值问题的上下解的定义,而且还证明了在该定义及Nagumo条件下的解的存在性定理,同时进一步得到了解的唯一性定理。

The existence of solution for three-point boundary value problem for second order differential equation are considered basing on the theory of differential inequalities of two-point boundary value problem for second order differential. Meanwhile, the corresponding defmition of supper and lower solution are presented. Also, the theorem of solution＇s existence is proofed under this defmition and Nagumo＇s condition. Furthermore, theroniqueness of solution is obtained.