Existence of asymptotically periodic solutions of system of Volterra difference equations

Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay

“…Periodicity of the solutions of difference equations has been handled by [2], [6]- [11]. In [7] and [8], the authors focused on a system of Volterra difference equations of the form…”

Explicit asymptotic limits for a class of discrete Volterra equations

“…Here, bð1Þ ¼ 23=7 and lim n!1 P n j¼0 hðn; jÞ ¼ 24=21, so that The particular solution considered in [1] corresponds to j ¼ 2 1 À Á T and…”

“…One motivation for this work was to explore the connection between the approaches used in Refs [1,2,5] for studying asymptotically periodic solutions of discrete Volterra equations.…”

Some stability conditions for scalar Volterra difference equations

“…Therefore, the qualitative theory of these types of equations is developed by many authors. For example, the boundedness of solutions of discrete Volterra equations was studied in [2,5,10] or [13]- [18], the periodicity was investigated in papers [6,8,15,18]. A survey of the fundamental results on the stability of linear Volterra difference equations, of both convolution and non-convolution type, can be found in [7], see also [3,4,11,12,17] or [19].…”