不动点原理及其应用

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题目： 不动点原理及其应用

摘要

本文主要讨论了压缩映射原理，Schauder不动点定理以及不动点的应用三个方面。在解决微分方程，积分方程，以及其他方程的解的存在唯一性时，将问题转换为求某一映射的不动点，利用不动点原理进行解决。

关键词：压缩映射原理；Schauder不动点定理； 不动点原理应用

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Abstract

In this paper ,we talked about contraction mapping principle,Schauder’s fixed point theorem and the application of the fixed point theorem.As we deal with the solutions about differential equation, integral equation and other kinds of equations, it is a useful way to transform the problem into fixed point theorem.We can use it to solve plenty of practice problems too.

Keywords: contraction mapping principle; Schauder’s fixed point theorem;the application of fixed point theorem.

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目录

引言 ........................................................................................................................ 1 1.压缩映射原理 .................................................................................................. 1

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1.1压缩映射原理（距离空间） ................................................................................... 1 1.2压缩映射原理（巴拿赫空间） .............................................................................. 7

2.Schauder不动点定理 .................................................................................... 9 3不动点定理的应用 ...................................................................................... 11 总结 ..................................................................................................................... 12 参考文献 ............................................................................................................ 14

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