@Article{Migda2016,
author = "Migda, Janusz and Migda, Małgorzata",
title = "Asymptotic behavior of solutions of discrete Volterra equations",
journal = "Opuscula Math.",
year = "2016",
volume = "36",
number = "2",
pages = "265--278",
doi = "http://dx.doi.org/10.7494/OpMath.2016.36.2.265",
url = "http://dx.doi.org/10.7494/OpMath.2016.36.2.265",
abstract = "We consider the nonlinear discrete Volterra equations of non-convolution type \[\Delta^m x_n=b_n+\sum\limits_{i=1}^{n}K(n,i)f\left(i,x_i\right), \quad n\geq 1.\] We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, especially asymptotically polynomial and asymptotically periodic solutions. We use \(\operatorname{o}(n^s)\), for a given nonpositive real \(s\), as a measure of approximation. We also give conditions under which all solutions are asymptotically polynomial.",
keywords = "Volterra difference equation, prescribed asymptotic behavior, asymptotically polynomial solution, asymptotically periodic solution, bounded solution",
issn = "1232-9274"
}