n阶非线性常微分方程n点边值问题解的存在唯一性

n阶非线性常微分方程n点边值问题解的存在唯一性早在20世纪50年代就有人开始研究，所得结果都是在条件及其复杂，假设了一些边值问题解的存在性或唯一性(甚至包括其自身的)的基础上得到的，这给应用带来了困难。至今还没有人得到条件简单明了的便于应用的存在唯一性定理。这篇文章成功地将上述边值问题转化成了积分方程问题．并利用格林函数，不动点定理得到了较好的存在唯一性结果。为研究n阶非线性常微分方程非线性n点边值问题奠定了基础。

Existence and uniqueness of solutions of n-point boundary value problems for n-order nonlinear differential equations

The existence and uniqneness of n-point boundary problem for the n-order differential equations was researched by some people early in twentieth century fifty years.The result was worked out on the base of complicated condition,presuming some boundany problems' existence or uniqueness(include it selfs),which leads to the difficulties of application.So far no one find out the existence and uniqueness theorem of clear and simple explaination and convenient to use.The article exchanges boundary problem to integral equation problem successfully,then making use of Green's function and unmoving point theorem gains better result of the existence and uniqueness.It establishes the basis of researching n-order nonlinear differential equations' and n-point boundany problem.