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Zbl 1202.39013
Dibl{\'\i}k, Josef; Schmeidel, Ewa; Ruužičková, Miroslava
Asymptotically periodic solutions of Volterra system of difference equations.
(English)
[J] Comput. Math. Appl. 59, No. 8, 2854-2867 (2010). ISSN 0898-1221

This paper is mainly concerned with the following system of Volterra difference equations: $$x_s(n+1)=a_s(n)+b_s(n)x_s(n)+\sum_{p=1}^r\sum_{i=0}^n K_{sp}(n,i)x_p(i),\quad s=1,2,\dots,r, \quad n=0,1,2,\dots.$$ By using Schauder's fixed point theorem, the authors prove that the above Volterra difference system has at least an asymptotically periodic solution. In addition, the author give several examples to illustrate their main results.
[Hui-Sheng Ding (Jiangxi)]
MSC 2000:
*39A23
39A30
39A06

Keywords: Volterra difference system; asymptotically periodic solution

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