Stable manifolds for non-instantaneous impulsive nonautonomous differential equations
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 un...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2019-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7394 |
| Summary: | 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 $C^{1}$ outside the jumping times using the continuous Fiber contraction principle technique. |
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| ISSN: | 1417-3875 |