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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
Descripción
Sumario: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.