Perron-Type Criterion for Linear Difference Equations with Distributed Delay

Alzabut, Jehad O.; Abdeljawad, Thabet

doi:https://doi.org/10.1155/2007/10840

Discrete Dynamics in Nature and Society

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Research Article | Open Access

Volume 2007 | Article ID 010840 | https://doi.org/10.1155/2007/10840

Perron-Type Criterion for Linear Difference Equations with Distributed Delay

Jehad O. Alzabut^1,2and Thabet Abdeljawad²

Received10 Apr 2007

Revised06 Jul 2007

Accepted17 Aug 2007

Published30 Oct 2007

Abstract

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.

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Copyright

Copyright © 2007 Jehad O. Alzabut and Thabet 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.

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