Existence of two-point oscillatory solutions of a relay nonautonomous system with a multiple eigenvalue of a real symmetric matrix
UDC 517.925 We study an $n$-dimensional system of ordinary differential equations with a hysteresis type relay nonlinearity and a periodic perturbation function in the right-hand side.It is supposed that the matrix of the system is real and symmetric and it has an eigenvalue of multiplicity two.In t...
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| Datum: | 2021 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6379 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.925
We study an $n$-dimensional system of ordinary differential equations with a hysteresis type relay nonlinearity and a periodic perturbation function in the right-hand side.It is supposed that the matrix of the system is real and symmetric and it has an eigenvalue of multiplicity two.In the phase space of the system, we consider continuous bounded oscillatory solutions with two fixed points and the same return time to each of these points.For such solutions, we prove the existence and nonexistence theorems.These results are illustrated by a numerical example for a three-dimensional system. |
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| DOI: | 10.37863/umzh.v73i5.6379 |