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

IF 1.1 4区数学 Q1 MATHEMATICS

Electronic Journal of Qualitative Theory of Differential Equations 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

Electronic Journal of Qualitative Theory of Differential Equations 数学-数学

CiteScore

1.40

自引率

9.10%

发文量

审稿时长

3 months

期刊介绍： The Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE) is a completely open access journal dedicated to bringing you high quality papers on the qualitative theory of differential equations. Papers appearing in EJQTDE are available in PDF format that can be previewed, or downloaded to your computer. The EJQTDE is covered by the Mathematical Reviews, Zentralblatt and Scopus. It is also selected for coverage in Thomson Reuters products and custom information services, which means that its content is indexed in Science Citation Index, Current Contents and Journal Citation Reports. Our journal has an impact factor of 1.827, and the International Standard Serial Number HU ISSN 1417-3875. All topics related to the qualitative theory (stability, periodicity, boundedness, etc.) of differential equations (ODE''s, PDE''s, integral equations, functional differential equations, etc.) and their applications will be considered for publication. Research articles are refereed under the same standards as those used by any journal covered by the Mathematical Reviews or the Zentralblatt (blind peer review). Long papers and proceedings of conferences are accepted as monographs at the discretion of the editors.