数学季刊 >

2024 , Vol. 39 >Issue 4: 420 - 430

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.04.008

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

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  • School Of Science, University of Science and Technology Liaoning, AnShan 114051, China
DENG Jing-tao (2003-), female, native of Chenzhou, Hunan, undergraduate student of University of Science and Technology Liaoning, engages in differential equations.

收稿日期: 2024-02-27

  网络出版日期: 2024-12-30

基金资助

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

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

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  • School Of Science, University of Science and Technology Liaoning, AnShan 114051, China
DENG Jing-tao (2003-), female, native of Chenzhou, Hunan, undergraduate student of University of Science and Technology Liaoning, engages in differential equations.

Received date: 2024-02-27

  Online published: 2024-12-30

Supported by

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

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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

本文引用格式

邓婧涛 . 一些非齐次常微分方程的 Hyers-Ulam 稳定性与 Hyers-Ulam 不稳定性[J]. 数学季刊, 2024 , 39(4) : 420 -430 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.008

Abstract

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.

Key words： Hyers-Ulam stability; Hyers-Ulam instability; Ordinary differential equations; Necessary and sufficient condition

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