Perron-Type Criterion for Linear Difference Equations With Distributed Delay

Abstract

It is shown that if a linear difference equation with distributed delay of the form Delta x(n) = Sigma(0)(k=-d)Delta(k)zeta(n + 1, k - 1)x(n + k - 1), n >= 1, satisfies a Perron condition then its trivial solution is uniformly asymptotically stable. Copyright (c) 2007 J. O. Alzabut and T. Abdeljawad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.