Method of local linear approximation in the theory of nonlinear impulsive systems
UDC 517.929 For nonlinear differential equations with impulsive perturbations, we formulate a general assertion concerning the existence of bounded solutions.  With the help of this assertion, we establish necessary and sufficient conditions for the existence and uniqueness...
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| Date: | 2023 |
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| Main Authors: | , , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7347 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.929
For nonlinear differential equations with impulsive perturbations, we formulate a general assertion concerning the existence of bounded solutions.  With the help of this assertion, we establish necessary and sufficient conditions for the existence and uniqueness of bounded solutions of analogous linear equations.  The equations are studied by using the theory of $c$-continuous operators and the method of local linear approximation of nonlinear equations. |
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| DOI: | 10.37863/umzh.v75i1.7347 |