具有周期系数的线性微分方程的Hyers-Ulam稳定性  

HYERS–ULAM STABILITY OF LINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

作　　者：董居悦 谢峰[1] DONG Ju-yue;XIE Feng(College of Science,Donghua University,Shanghai 201620,China)

机构地区：[1]东华大学理学院,上海201620

出　　处：《数学杂志》2024年第3期225-235,共11页Journal of Mathematics

基　　金：上海市自然科学基金资助(21ZR1401000)。

摘　　要：本文研究了具有周期系数的一阶和二阶线性微分方程的Hyers-Ulam稳定性.利用常数变易法,获得了其Hyers-Ulam稳定性的充分必要条件,推广了具有周期系数的一阶齐次线性微分方程Hyers-Ulam稳定性的相关结果.This paper deals with Hyers-Ulam stability(HUS)of first and second order linear differential equations with periodic coefficients.Necessary and sufficient conditions are established for Hyers-Ulam stability of the linear differential equations by means of the constant variation method.The related results of Hyers-Ulam stability for first order homogeneous linear differential equations with periodic coefficients are generalized.

关 键 词：Ulam型稳定性 线性微分方程 周期系数 充要条件 

分 类 号：O175.13[理学—数学]