Perron-Type Criterion for Linear Difference Equations with Distributed Delay - Jehad O. Alzabut; Thabet Abdeljawad (Discrete Dynamics in Nature and Society)
It is shown that if a linear difference equation with distributed delay of the form Δx(n)=∑k=−d0Δkζ(n+1,k−1)x(n+k−1), n≥1, satisfies a Perron condition then its trivial solution is uniformly asymptotically stable.