一类非线性三阶边值问题解的存在性

The Existence of Solution to a Third-order Boundary Value Problem

通过新的极大值原理及上下解的单调迭代方法讨论了三阶非线性边值问题{-u″′(t)=f(t,u(t)),t∈[0,1],u(0)=u'(0)=u(1)=0.解的存在性,其中f(t,u):[0,1]×R→R为连续函数.在非线性项f关于u满足适当单调条件的时,获得了解的存在性结果.

A new maximum principle and monotone iterative method of lower and upper solutions are employed to establish existence result for the third -- order boundary value problem {-u^″′（t）=f（t,u（t））,t∈[0,1], u（0）=u′（0）=u（1）=0. where f（t,u） ：[0,1] ×R → R is continuous. In the case that f satisfies appropriate monotone condition about u,the author obtains the existence results of solutions.