Shadowing, Hyers–Ulam stability and hyperbolicity for nonautonomous linear delay differential equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-27 DOI:10.1142/s0219199724500123

Lucas Backes, Davor Dragičević, Mihály Pituk

引用次数: 0

Abstract

It is known that hyperbolic nonautonomous linear delay differential equations in a finite dimensional space are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example.

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非自治线性延迟微分方程的阴影、海尔-乌兰稳定性和双曲性

众所周知，有限维空间中的双曲非自治线性延迟微分方程是海尔-乌兰稳定的，因此是可影的。只有在具有简单谱的自洽周期线性延迟微分方程的特殊情况下，才有相反的结果。在本文中，我们证明了反向结果，进而证明了标题中所有三个概念对于一类具有均匀有界系数的非自治线性延迟微分方程的等价性。有界性假设的重要性将通过一个例子来说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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