On the solution manifold of a differential equation with a delay which has a zero

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2022-05-02 DOI:10.14232/ejqtde.2022.1.31

H. Walther

引用次数: 1

Abstract

For a differential equation with a state-dependent delay we show that the associated solution manifold X f of codimension 1 in the space C 1 ( [ − r , 0 ] , R ) is an almost graph over a hyperplane, which implies that X f is diffeomorphic to the hyperplane. For the case considered previous results only provide a covering by 2 almost graphs.

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时滞为零的微分方程的解流形

对于具有状态相关延迟的微分方程，我们证明了空间C1（[-r，0]，r）中余维1的相关解流形Xf是超平面上的概图，这意味着Xf与超平面是微分同胚的。对于所考虑的情况，先前的结果只提供了2个几乎图的覆盖。

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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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