About: Existence of unbounded solutions of a linear homogenous system of differential equations with two delays

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10243
Description	Asymptotic behavior of solutions of a linear homogeneous system of differential equations with deviating arguments in the form \dot y(t)=\beta(t)\left[y(t-\delta)-y(t-\tau)\right] is discussed for t\to\infty. It is assumed that y is an n-dimensional column vector, n>1$is an integer, \delta,\tau\in{\mathbb{R}}, \tau>\delta>0 and \beta(t) is an n\times n matrix defined for t\geq t_{0}, t_{0}\in\mathbb{R}, and such that its elements are nonnegative, continuous functions and in every row of this matrix is each time at least one element nonzero. The existence of solutions in an exponential form under certain assumptions is proved. Sufficient conditions for the existence of unbounded solutions are derived. The estimations for a solution are given and the scalar case is discussed as well. Asymptotic behavior of solutions of a linear homogeneous system of differential equations with deviating arguments in the form \dot y(t)=\beta(t)\left[y(t-\delta)-y(t-\tau)\right] is discussed for t\to\infty. It is assumed that y is an n-dimensional column vector, n>1$is an integer, \delta,\tau\in{\mathbb{R}}, \tau>\delta>0 and \beta(t) is an n\times n matrix defined for t\geq t_{0}, t_{0}\in\mathbb{R}, and such that its elements are nonnegative, continuous functions and in every row of this matrix is each time at least one element nonzero. The existence of solutions in an exponential form under certain assumptions is proved. Sufficient conditions for the existence of unbounded solutions are derived. The estimations for a solution are given and the scalar case is discussed as well. (en)
Title	Existence of unbounded solutions of a linear homogenous system of differential equations with two delays Existence of unbounded solutions of a linear homogenous system of differential equations with two delays (en)
skos:prefLabel	Existence of unbounded solutions of a linear homogenous system of differential equations with two delays Existence of unbounded solutions of a linear homogenous system of differential equations with two delays (en)
skos:notation	RIV/00216305:26110/14:PU111009!RIV15-MSM-26110___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(ED2.1.00/03.0097)
http://linked.open...iv/cisloPeriodika	2014
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Diblík, 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	Vysoké učení technické v Brně / Fakulta stavební
http://linked.open...dnocenehoVysledku	15705
http://linked.open...ai/riv/idVysledku	RIV/00216305:26110/14:PU111009
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	system of differential equations, unbounded solution, exponential solution, delay (en)
http://linked.open.../riv/klicoveSlovo	system of differential equations delay exponential solution unbounded solution
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[D937F240AF60]
http://linked.open...i/riv/nazevZdroje	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	AdMaS - Advanced Materials, Structures and Technologies
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	19
http://linked.open...iv/tvurceVysledku	Diblík, Josef Růžičková, Miroslava Chupáč, Radoslav
http://linked.open...ain/vavai/riv/wos	000341776200007
issn	1531-3492
number of pages	13 (xsd:int)
http://bibframe.org/vocab/doi	10.3934/dcdsb.2014.19.2447
http://localhost/t...ganizacniJednotka	26110

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