About: Asymptotic convergence of the solutions of a discrete system with delays

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	A system of $s$ discrete equations \begin{equation} \Delta y (n)=\beta(n)[y(n-j)-y(n-k)] \end{equation} is considered where $k$ and $j$ are integers, $k>j\geq0$, $\beta(n)$ is a real $s\times s$ square matrix defined for $n\ge n_{0}-k$, $n_{0}\in \mathbb{Z}$ with non-negative elements $\beta _{ij}(n)$, $i,j=1,\dots,s$ such that $\sum_{j=1}^{s}\beta _{ij}(n)>0$, $y=(y_1, y_2,\dots,y_s)^T\colon {n_{0}-k,n_{0}-k+1,\dots\}\to \mathbb{R}^{s}$ and $\Delta y(n)=y(n+1)-y(n)$ for $n\ge n_{0}$. A method of auxiliary inequalities is used to prove that every solution of the given system is asymptotically convergent under some conditions, i.e., for every solution $y(n)$ defined for all sufficiently large $n$, there exists a finite limit $\lim_{n\to\infty}y(n)$. Moreover, it is proved that the asymptotic convergence of all solutions is equivalent to the existence of one asymptotically convergent solution with increasing coordinates. Some discussion related to the so-called critical case known for scalar equa A system of $s$ discrete equations \begin{equation} \Delta y (n)=\beta(n)[y(n-j)-y(n-k)] \end{equation} is considered where $k$ and $j$ are integers, $k>j\geq0$, $\beta(n)$ is a real $s\times s$ square matrix defined for $n\ge n_{0}-k$, $n_{0}\in \mathbb{Z}$ with non-negative elements $\beta _{ij}(n)$, $i,j=1,\dots,s$ such that $\sum_{j=1}^{s}\beta _{ij}(n)>0$, $y=(y_1, y_2,\dots,y_s)^T\colon {n_{0}-k,n_{0}-k+1,\dots\}\to \mathbb{R}^{s}$ and $\Delta y(n)=y(n+1)-y(n)$ for $n\ge n_{0}$. A method of auxiliary inequalities is used to prove that every solution of the given system is asymptotically convergent under some conditions, i.e., for every solution $y(n)$ defined for all sufficiently large $n$, there exists a finite limit $\lim_{n\to\infty}y(n)$. Moreover, it is proved that the asymptotic convergence of all solutions is equivalent to the existence of one asymptotically convergent solution with increasing coordinates. Some discussion related to the so-called critical case known for scalar equa (en)
Title	Asymptotic convergence of the solutions of a discrete system with delays Asymptotic convergence of the solutions of a discrete system with delays (en)
skos:prefLabel	Asymptotic convergence of the solutions of a discrete system with delays Asymptotic convergence of the solutions of a discrete system with delays (en)
skos:notation	RIV/00216305:26110/12:PU101101!RIV14-GA0-26110___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(ED2.1.00/03.0097), P(GAP201/10/1032)
http://linked.open...iv/cisloPeriodika	18
http://linked.open...vai/riv/dodaniDat	2014
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	123968
http://linked.open...ai/riv/idVysledku	RIV/00216305:26110/12:PU101101
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Discrete equation, delay, asymptotic convergence, increasing solution. (en)
http://linked.open.../riv/klicoveSlovo	delay asymptotic convergence increasing solution. Discrete equation
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[6EF0D776A7AE]
http://linked.open...i/riv/nazevZdroje	APPLIED MATHEMATICS AND COMPUTATION
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	Difference equations and dynamic equations on time scales III AdMaS - Advanced Materials, Structures and Technologies
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	2012
http://linked.open...iv/tvurceVysledku	Diblík, Josef Růžičková, Miroslava Šutá, Zuzana
issn	0096-3003
number of pages	9 (xsd:int)
http://localhost/t...ganizacniJednotka	26110

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