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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...

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Detalles Bibliográficos
Autores principales: Lu, Weijie, Pinto, Manuel, Xia, Yonghui
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2022
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.
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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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