一类非线性三阶边值问题的单调迭代方法

Monotone Iterative Method for a Nonlinear Third-Order Boundary Value Problem

运用上下解的单调迭代方法讨论三阶常微分方程边值问题-u″′(t)=f(t,u(t),u′(t)),t∈[0,1]u(0)=u′(0)=u′(1)=0解的存在性,其中f(t,u,v):[0,1]×R×R→R为连续函数.在f关于u,v满足较弱单调条件的情形下。

In this paper, by using the monotone iterative method we discuss the existence of the solutions for the third-order boundary value problem {-U＇＇（t）=f（t,u（t）,u＇（t））,t∈[0,1] u（0）=u＇（0）=u＇（1）=0} where f（t, u, v） ：[0,1] × R × R → is continuous. If f satisfies weaker monotone conditions about u and v, the authors establish a new maximum principle and obtain the existence results of the solutions.