On the existence of solutions of linear Volterra difference equations asymptotically equivalent to a given sequence

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F12%3APU97719" target="_blank" >RIV/00216305:26110/12:PU97719 - 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

On the existence of solutions of linear Volterra difference equations asymptotically equivalent to a given sequence

Original language description

Schauder's fixed point technique is applied to asymptotical analysis of solutions of a linear Volterra difference equation $$ x(n+1)=a(n)+b(n)x(n)+sumlimits^{n}_{i=0}K(n,i)x(i) $$ where $nin bN_0$, $xcolonbN_0tobR$, $acolon bN_0tobR$, $KcolonbN_0timesbN_0to bR$, and $bcolonbN_0 to bRsetminus{0}$ is $omega$-periodic. In the paper, sufficient conditions are derived for the validity of a property of solutions that, for every admissible constant $cin bR$, there exists a solution$x=x(n)$ such that $$ {x(n){sim}}left(c+sumlimits_{i=0}^{n-1}frac{a(i)}{beta(i+1)}right)beta(n),$$ where $beta(n)=prodlimits_{j=0}^{n-1}b(j)$, for $ntoinfty$ and inequalities for solutions are derived. Relevant comparisons and illustrative examples are given as well.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Difference equations and dynamic equations on time scales III</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

APPLIED MATHEMATICS AND COMPUTATION

ISSN

0096-3003

e-ISSN

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Volume of the periodical

2012

Issue of the periodical within the volume

18

Country of publishing house

US - UNITED STATES

Number of pages

11

Pages from-to

9310-9320

UT code for WoS article

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EID of the result in the Scopus database

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