Stable manifolds for non-instantaneous impulsive nonautonomous differential equations

Mengmeng Li; Jinrong Wang; Donal O’regan

doi:10.14232/ejqtde.2019.1.82

Stable manifolds for non-instantaneous impulsive nonautonomous differential equations

Mengmeng Li, Jinrong Wang, Donal O’regan

Mathematics

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7 Citations (Scopus)

Abstract

In this paper, we study stable invariant manifolds for a class of nonautonomous non-instantaneous impulsive equations where the homogeneous part has a nonuniform exponential dichotomy. We establish a stable invariant manifold result for sufficiently small perturbations by constructing stable and unstable invariant manifolds and we also show that the stable invariant manifolds are of class C¹ outside the jumping times using the continuous Fiber contraction principle technique.

Original language	English
Article number	82
Number of pages	27
Journal	Electronic Journal of Qualitative Theory of Differential Equations
Volume	2019
DOIs	https://doi.org/10.14232/ejqtde.2019.1.82
Publication status	Published - 1 Jan 2019

Keywords

Invariant manifolds
Non-instantaneous impulsive equations
Nonuniform exponential dichotomy

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Li, MM;Wang, JR;O'Regan, D

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10.14232/ejqtde.2019.1.82

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abstract = "In this paper, we study stable invariant manifolds for a class of nonautonomous non-instantaneous impulsive equations where the homogeneous part has a nonuniform exponential dichotomy. We establish a stable invariant manifold result for sufficiently small perturbations by constructing stable and unstable invariant manifolds and we also show that the stable invariant manifolds are of class C1 outside the jumping times using the continuous Fiber contraction principle technique.",

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AU - O’regan, Donal

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N2 - In this paper, we study stable invariant manifolds for a class of nonautonomous non-instantaneous impulsive equations where the homogeneous part has a nonuniform exponential dichotomy. We establish a stable invariant manifold result for sufficiently small perturbations by constructing stable and unstable invariant manifolds and we also show that the stable invariant manifolds are of class C1 outside the jumping times using the continuous Fiber contraction principle technique.

AB - In this paper, we study stable invariant manifolds for a class of nonautonomous non-instantaneous impulsive equations where the homogeneous part has a nonuniform exponential dichotomy. We establish a stable invariant manifold result for sufficiently small perturbations by constructing stable and unstable invariant manifolds and we also show that the stable invariant manifolds are of class C1 outside the jumping times using the continuous Fiber contraction principle technique.

KW - Invariant manifolds

KW - Non-instantaneous impulsive equations

KW - Nonuniform exponential dichotomy

UR - https://www.scopus.com/pages/publications/85076274345

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DO - 10.14232/ejqtde.2019.1.82

M3 - Article

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JO - Electronic Journal of Qualitative Theory of Differential Equations

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M1 - 82

ER -

Stable manifolds for non-instantaneous impulsive nonautonomous differential equations

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

Access to Document

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