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Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators
In this paper, we present a theory of smooth stable manifold for the non-instantaneous impulsive differential equations on the Banach space or Hilbert space. Assume that the non-instantaneous linear impulsive evolution differential equation admits a uniform exponential dichotomy, we give the conditi...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8941643/ https://www.ncbi.nlm.nih.gov/pubmed/35350816 http://dx.doi.org/10.1098/rspa.2021.0957 |
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author | Lu, Weijie Pinto, Manuel Xia, Yonghui |
author_facet | Lu, Weijie Pinto, Manuel Xia, Yonghui |
author_sort | Lu, Weijie |
collection | PubMed |
description | In this paper, we present a theory of smooth stable manifold for the non-instantaneous impulsive differential equations on the Banach space or Hilbert space. Assume that the non-instantaneous linear impulsive evolution differential equation admits a uniform exponential dichotomy, we give the conditions of the existence of the global and local stable manifolds. Furthermore, [Formula: see text]-smoothness of the stable manifold is obtained, and the periodicity of the stable manifold is given. Finally, an application to nonlinear Duffing oscillators with non-instantaneous impulsive effects is given, to demonstrate the existence of stable manifold. |
format | Online Article Text |
id | pubmed-8941643 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-89416432022-03-28 Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators Lu, Weijie Pinto, Manuel Xia, Yonghui Proc Math Phys Eng Sci Research Articles In this paper, we present a theory of smooth stable manifold for the non-instantaneous impulsive differential equations on the Banach space or Hilbert space. Assume that the non-instantaneous linear impulsive evolution differential equation admits a uniform exponential dichotomy, we give the conditions of the existence of the global and local stable manifolds. Furthermore, [Formula: see text]-smoothness of the stable manifold is obtained, and the periodicity of the stable manifold is given. Finally, an application to nonlinear Duffing oscillators with non-instantaneous impulsive effects is given, to demonstrate the existence of stable manifold. The Royal Society 2022-03 2022-03-23 /pmc/articles/PMC8941643/ /pubmed/35350816 http://dx.doi.org/10.1098/rspa.2021.0957 Text en © 2022 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Research Articles Lu, Weijie Pinto, Manuel Xia, Yonghui Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators |
title | Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators |
title_full | Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators |
title_fullStr | Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators |
title_full_unstemmed | Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators |
title_short | Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators |
title_sort | smooth stable manifolds for the non-instantaneous impulsive equations with applications to duffing oscillators |
topic | Research Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8941643/ https://www.ncbi.nlm.nih.gov/pubmed/35350816 http://dx.doi.org/10.1098/rspa.2021.0957 |
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