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The Existence of Periodic Solutions for Second-Order Delay Differential Systems
In this paper, we consider a kind of second-order delay differential system. By taking some transforms, the property of delay is reflected in the boundary condition. The wonder is that the corrseponding first-order system is exactly the so-called P-boundary value problem of Hamiltonian system which...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer US
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9667453/ https://www.ncbi.nlm.nih.gov/pubmed/36407964 http://dx.doi.org/10.1007/s10884-022-10226-2 |
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author | Liu, Chungen Wang, Qi |
author_facet | Liu, Chungen Wang, Qi |
author_sort | Liu, Chungen |
collection | PubMed |
description | In this paper, we consider a kind of second-order delay differential system. By taking some transforms, the property of delay is reflected in the boundary condition. The wonder is that the corrseponding first-order system is exactly the so-called P-boundary value problem of Hamiltonian system which has been studied deeply by many mathematicians, including the authors of this paper. Firstly, we define the relative Morse index [Formula: see text] for the delay system and give the relationship with the P-index [Formula: see text] of Hamiltonian system. Secondly, by this index, topology degree and saddle point reduction, the existence of periodic solutions is established for this kind of delay differential system. |
format | Online Article Text |
id | pubmed-9667453 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-96674532022-11-16 The Existence of Periodic Solutions for Second-Order Delay Differential Systems Liu, Chungen Wang, Qi J Dyn Differ Equ Article In this paper, we consider a kind of second-order delay differential system. By taking some transforms, the property of delay is reflected in the boundary condition. The wonder is that the corrseponding first-order system is exactly the so-called P-boundary value problem of Hamiltonian system which has been studied deeply by many mathematicians, including the authors of this paper. Firstly, we define the relative Morse index [Formula: see text] for the delay system and give the relationship with the P-index [Formula: see text] of Hamiltonian system. Secondly, by this index, topology degree and saddle point reduction, the existence of periodic solutions is established for this kind of delay differential system. Springer US 2022-11-16 /pmc/articles/PMC9667453/ /pubmed/36407964 http://dx.doi.org/10.1007/s10884-022-10226-2 Text en © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Liu, Chungen Wang, Qi The Existence of Periodic Solutions for Second-Order Delay Differential Systems |
title | The Existence of Periodic Solutions for Second-Order Delay Differential Systems |
title_full | The Existence of Periodic Solutions for Second-Order Delay Differential Systems |
title_fullStr | The Existence of Periodic Solutions for Second-Order Delay Differential Systems |
title_full_unstemmed | The Existence of Periodic Solutions for Second-Order Delay Differential Systems |
title_short | The Existence of Periodic Solutions for Second-Order Delay Differential Systems |
title_sort | existence of periodic solutions for second-order delay differential systems |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9667453/ https://www.ncbi.nlm.nih.gov/pubmed/36407964 http://dx.doi.org/10.1007/s10884-022-10226-2 |
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