Asymptotic convergence of the solutions of a discrete system with delays

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F12%3APU101101" target="_blank" >RIV/00216305:26110/12:PU101101 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Asymptotic convergence of the solutions of a discrete system with delays
Original language 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, $k>jgeq0$, $beta(n)$ is a real $stimes s$ square matrix defined for $nge n_{0}-k$, $n_{0}in mathbb{Z}$ with non-negative elements $beta _{ij}(n)$, $i,j=1,dots,s$ such that $sum_{j=1}^{s}beta _{ij}(n)>0$, $y=(y_1, y_2,dots,y_s)^Tcolon {n_{0}-k,n_{0}-k+1,dots}to mathbb{R}^{s}$ and $Delta y(n)=y(n+1)-y(n)$ for $nge n_{0}$. 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 $lim_{ntoinfty}y(n)$. 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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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