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Statements

Subject Item
n2:RIV%2F00216305%3A26110%2F14%3APU111009%21RIV15-MSM-26110___
rdf:type
skos:Concept n16:Vysledek
rdfs:seeAlso
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10243
dcterms: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.
dcterms: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
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
skos:notation
RIV/00216305:26110/14:PU111009!RIV15-MSM-26110___
n4:aktivita
n20:P
n4:aktivity
P(ED2.1.00/03.0097)
n4:cisloPeriodika
2014
n4:dodaniDat
n12:2015
n4:domaciTvurceVysledku
n8:4066227
n4:druhVysledku
n17:J
n4:duvernostUdaju
n6:S
n4:entitaPredkladatele
n5:predkladatel
n4:idSjednocenehoVysledku
15705
n4:idVysledku
RIV/00216305:26110/14:PU111009
n4:jazykVysledku
n13:eng
n4:klicovaSlova
system of differential equations, unbounded solution, exponential solution, delay
n4:klicoveSlovo
n10:system%20of%20differential%20equations n10:delay n10:unbounded%20solution n10:exponential%20solution
n4:kodStatuVydavatele
US - Spojené státy americké
n4:kontrolniKodProRIV
[D937F240AF60]
n4:nazevZdroje
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
n4:obor
n9:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
3
n4:projekt
n11:ED2.1.00%2F03.0097
n4:rokUplatneniVysledku
n12:2014
n4:svazekPeriodika
19
n4:tvurceVysledku
Růžičková, Miroslava Chupáč, Radoslav Diblík, Josef
n4:wos
000341776200007
s:issn
1531-3492
s:numberOfPages
13
n19:doi
10.3934/dcdsb.2014.19.2447
n15:organizacniJednotka
26110