Asymptotically periodic solutions of Volterra system of difference equations. (English) Zbl 1202.39013

Diblík, Josef; Schmeidel, Ewa; Růžičková, Miroslava

Comput. Math. Appl. 59, No. 8, 2854-2867 (2010).

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.

Reviewer: Hui-Sheng Ding (Jiangxi)

MSC:

39A23	Periodic solutions of difference equations
39A30	Stability theory for difference equations
39A06	Linear difference equations

Keywords:

Volterra difference system; asymptotically periodic solution

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