Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case
| Název česky | Asymptoptické chování řešení reálného dvojrozměrného diferenciálního systému s nekonstantním zpožděním v nestabilním případě |
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| Autoři | |
| Rok publikování | 2012 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Electronic Journal of Qualitative Theory of Differential Equations |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=612 |
| Obor | Obecná matematika |
| Klíčová slova | Delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle |
| Popis | The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for t approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle. |
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