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Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators.

ABSTRACT: 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, Ck -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.

SUBMITTER: Lu W

PROVIDER: S-EPMC8941643 | biostudies-literature | 2022 Mar

REPOSITORIES: biostudies-literature

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Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators.

Lu Weijie W Pinto Manuel M Xia Yonghui Y

Proceedings. Mathematical, physical, and engineering sciences 20220323 2259

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, C k -smoothness of the stable manifold is obtained, and the periodicity of the stable manifold is given. Finally, an appli ...[more]

PMID: 35350816

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