一类不动点定理及其在微分方程中的应用  

A Fixed Point Theorem and Its Application to Differential Equations

作　　者：陈晓玲 李慧 贺飞[1] CHEN Xiaoling;LI Hui;HE Fei(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《应用泛函分析学报》2020年第1期66-71,共6页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11561049)。

摘　　要：在完备的距离空间中,建立了一类含有广义变距离函数的压缩映射不动点定理.将这一结果应用于一阶常微分方程周期边值问题中,得到了方程存在唯一解的充分条件.我们的结果比已有结果的条件更弱且完全去掉了下解存在的条件.In complete metric spaces,a fixed point theorem of contractive mapping with generalized altering distance functions is established.Applying our result to the first-order ordinary differential equation with periodic boundary value,we obtain sufficient conditions for the existence of unique solutions of the equations.Our results are weaker than the existing results and completely remove the condition for the existence of the lower solution.

关 键 词：距离空间 广义变距离函数 不动点定理 一阶常微分方程 周期边值问题 

分 类 号：O177.91[理学—数学]