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Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case

Basic information
Original title:Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case
Authors:Josef Kalas, Josef Rebenda
Further information
Citation:KALAS, Josef and Josef REBENDA. Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case. Electronic Journal of Qualitative Theory of Differential Equations, Szeged, 2012, Neuveden, No 8, p. 1-19. ISSN 1417-3875.Export BibTeX
@article{967835,
author = {Kalas, Josef and Rebenda, Josef},
article_location = {Szeged},
article_number = {8},
keywords = {Delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle},
language = {eng},
issn = {1417-3875},
journal = {Electronic Journal of Qualitative Theory of Differential Equations},
title = {Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case},
url = {http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=612},
volume = {Neuveden},
year = {2012}
}
Original language:English
Field:General mathematics
WWW:link to a new windowhttp://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=612
Type:Article in Periodical
Keywords:Delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle

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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