关于非线性边值问题几个存在性定理的新结果

New Results of Some Existence Theorems on Nonlinear Boundary Value Problems

本文运用同胚理论，研究微分方程边值问题解的存在性与唯一性，得到两个基本定理，推广了Ｂｒｏｗｎ（ｉｎＡｎｎａｌｉ．Ｍａｔ．Ｐｕｒａ．Ａｐｐｌｉ．１９７５，１０６：２０５～２１４）的结论，取消了有界性假设，并把我们的结果用于有限维的情况。

With the use of the homeomorohism theory and fixed point theory, the existence and uniqueness of solutions to boundary value problems are investigated. Two basic theorems are obtained without the boundness condition, which generalizes results of Brown. When our results are applied to the existence and uniqueness of periodic solutions for nonlinear perturbed conservative systems (Newtonian equations of motion), the existence and uniqueness of the solution obtained. The results in this note seem less restrictive than those of the former papers we have seen. Mean while, as far as we know, it seems that applying the homeomorphism theory to the research of this kind of problem is new.