一类二阶三点边值问题单调正解的存在性

Existence of Monotone Positive Solutions to a Type of Three-point Boundary Value Problem

利用范数形式的锥上不动点定理,研究了一类二阶微分方程三点边值问题单调正解的存在性．分别给出了齐次和非齐次边界条件下的三点边值问题单调正解存在的充分条件,确定了解曲线的凹凸性,并且给出了一个应用实例．

This paper studies the existence of monotone positive solutions to a type of three point boundary value problems of nonlinear second-order differential equations. By use of the stretch and compression fixed point theorem of normic form in cone, the sufficient conditions for the existence of monotone positive solutions are given to the boundary value problems with homogeneous and nonhomogeneous boundary conditions, respectively. An example is also given to illustrate the effectiveness of our results.