{"title":"On the solution manifold of a differential equation with a delay which has a zero","authors":"H. Walther","doi":"10.14232/ejqtde.2022.1.31","DOIUrl":null,"url":null,"abstract":"For a differential equation with a state-dependent delay we show that the associated solution manifold \n \n X\n f\n \n of codimension 1 in the space \n \n C\n 1\n \n (\n [\n −\n r\n ,\n 0\n ]\n ,\n \n R\n \n )\n is an almost graph over a hyperplane, which implies that \n \n X\n f\n \n is diffeomorphic to the hyperplane. For the case considered previous results only provide a covering by 2 almost graphs.","PeriodicalId":50537,"journal":{"name":"Electronic Journal of Qualitative Theory of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Qualitative Theory of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.14232/ejqtde.2022.1.31","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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