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

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Authors	KALAS Josef REBENDA Josef
Year of publication	2012
Type	Article in Periodical
Magazine / Source	Electronic Journal of Qualitative Theory of Differential Equations
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=612
Field	General mathematics
Keywords	Delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle
Description	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.
Related projects:	Oscillatory and asymptotic properties of solutions of differential equations