About: Asymptotic behaviour of a two-dimensional differential system with delay under the conditions of instability

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The asymptotic behaviour of the solutions of a real two-dimensional system x'=A(t)x(t)+B(t)x(t-r)+h(t,x(t),x(t-r)), where r>0 is a constant delay, is studied under the assumption of instability. Here A, B and h are matrix functions and a vector function, respectively. The conditions for the existence of bounded solutions or solutions tending to the origin as t 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 LyapunovKrasovskii functional and by virtue of the Wazewski topological principle. The results supplement those of Kalas and Baráková [J. Math. Anal. Appl. 269(1)(2002) 278300], where the stability and asymptotic behaviour were investigated for the stable case. The asymptotic behaviour of the solutions of a real two-dimensional system x'=A(t)x(t)+B(t)x(t-r)+h(t,x(t),x(t-r)), where r>0 is a constant delay, is studied under the assumption of instability. Here A, B and h are matrix functions and a vector function, respectively. The conditions for the existence of bounded solutions or solutions tending to the origin as t 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 LyapunovKrasovskii functional and by virtue of the Wazewski topological principle. The results supplement those of Kalas and Baráková [J. Math. Anal. Appl. 269(1)(2002) 278300], where the stability and asymptotic behaviour were investigated for the stable case. (en)
Title	Asymptotic behaviour of a two-dimensional differential system with delay under the conditions of instability Asymptotic behaviour of a two-dimensional differential system with delay under the conditions of instability (en)
skos:prefLabel	Asymptotic behaviour of a two-dimensional differential system with delay under the conditions of instability Asymptotic behaviour of a two-dimensional differential system with delay under the conditions of instability (en)
skos:notation	RIV/00216224:14310/05:00013383!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA1163401), Z(MSM 143100001)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Kalas, Josef
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	513239
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/05:00013383
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Delayed differential equation; Asymptotic behaviour; Boundedness of solutions; Two-dimensional systems; Lyapunov method; Wazewski topological principle (en)
http://linked.open.../riv/klicoveSlovo	Delayed differential equation Lyapunov method Wazewski topological principle Asymptotic behaviour Two-dimensional systems Boundedness of solutions
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[2CD6526411C1]
http://linked.open...i/riv/nazevZdroje	Nonlinear Analysis, Theory, Methods & Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Limit properties of solutions of differential equations
http://linked.open...UplatneniVysledku	2005
http://linked.open...v/svazekPeriodika	62
http://linked.open...iv/tvurceVysledku	Kalas, Josef
http://linked.open...ain/vavai/riv/wos	000229983100002
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20143100001
issn	0362-546X
number of pages	18 (xsd:int)
http://localhost/t...ganizacniJednotka	14310
is http://linked.open...avai/riv/vysledek of	Asymptotic behaviour of a two-dimensional differential system with delay under the conditions of instability

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