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

This paper is mainly concerned with the following system of Volterra difference equations:

${x}_{s}\left(n+1\right)={a}_{s}\left(n\right)+{b}_{s}\left(n\right){x}_{s}\left(n\right)+\sum _{p=1}^{r}\sum _{i=0}^{n}{K}_{sp}\left(n,i\right){x}_{p}\left(i\right),\phantom{\rule{1.em}{0ex}}s=1,2,\cdots ,r,\phantom{\rule{1.em}{0ex}}n=0,1,2,\cdots ·$

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.

MSC:
 39A23 Periodic solutions (difference equations) 39A30 Stability theory (difference equations) 39A06 Linear equations (difference equations)
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