The Hyers-Ulam Stability and Hyers-Ulam Instability for Some Nonhomogeneous Ordinary Differential Equations  

一些非齐次常微分方程的Hyers-Ulam稳定性与Hyers-Ulam不稳定性

作　　者：DENG Jing-tao 邓婧涛

机构地区：[1]School Of Science,University of Science and Technology Liaoning,AnShan 114051,China

出　　处：《Chinese Quarterly Journal of Mathematics》2024年第4期420-430,共11页数学季刊（英文版）

基　　金：Supported by Natural Science Research Projects of Liaoning Province Education Department(Grant No.LJ212410146024).

摘　　要：In this paper,we get a necessary and sufficient condition such that a class of differential inequalities hold.Using this necessary and sufficient condition,we prove that a class of first order nonhomogeneous ordinary differential equations have the Hyers-Ulam stability.And then,we prove that some first order nonhomogeneous ordinary differential equations and some second order nonhomogeneous ordinary differential equations do not have the Hyers-Ulam instability under some suitable conditions.

关 键 词：Hyers-Ulam stability Hyers-Ulam instability Ordinary differential equations Necessary and sufficient condition 

分 类 号：O175.1[理学—数学]