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Weighted asymptotically periodic solutions of linear Volterra difference equations. (English) Zbl 1220.39016

Summary: A linear Volterra difference equation of the form \(x(n + 1) = a(n) + b(n)x(n) + \sum^n_{i=0} K(n, i)x(i)\), where \(x : \mathbb N_0 \rightarrow \mathbb R\), \(a : \mathbb N_0 \rightarrow \mathbb R\), \(K : \mathbb N_0 \times \mathbb N_0 \rightarrow \mathbb R\) and \(b : \mathbb N_0 \rightarrow \mathbb R \setminus \{ 0 \}\) is \(\omega\)-periodic, is considered. Sufficient conditions for the existence of weighted asymptotically periodic solutions of this equation are obtained. Unlike previous investigations, no restriction on \(\prod^{\omega-1}_{j=0} b(j)\) is assumed. The results generalize some of the recent results.

MSC:

39A23 Periodic solutions of difference equations
39A06 Linear difference equations
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