Advances in Difference Equations
Volume 2008 (2008), Article ID 598964, 15 pages
Uniform Asymptotic Stability and Robust Stability for Positive Linear Volterra Difference Equations in Banach Lattices
1Department of Applied Mathematics, Okayama University of Science, 1-1 Ridaicho, Okayama 700-0005, Japan
2Department of Applied Science, Okayama University of Science, 1-1 Ridaicho, Okayama 700-0005, Japan
Received 5 August 2008; Accepted 7 November 2008
Academic Editor: Ulrich Krause
Copyright © 2008 Satoru Murakami and Yutaka Nagabuchi. 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.
For positive linear Volterra difference equations in Banach lattices, the uniform
asymptotic stability of the zero solution is studied in connection with the summability of the
fundamental solution and the invertibility of the characteristic operator associated with the
equations. Moreover, the robust stability is discussed and some stability radii are given explicitly.