Advances in Difference Equations
Volume 2006 (2006), Article ID 58453, 14 pages
doi:10.1155/ADE/2006/58453
Exponential dichotomy of difference equations in lp-phase spaces on the half-line
Department of Applied Mathematics, Hanoi University of Technology, Khoa Toan Ung Dung, Dai Hoc Bach Khoa Ha Noi, 1 Dai Co Viet Street, Hanoi, Vietnam
Received 14 November 2005; Revised 12 March 2006; Accepted 17 May 2006
Copyright © 2006 Nguyen Thieu Huy and Vu Thi Ngoc Ha. 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.
Abstract
For a sequence of bounded linear operators
{An}n=0∞ on a Banach space X, we investigate the characterization of exponential dichotomy of the difference equations vn+1=Anvn. We characterize the exponential dichotomy of difference equations
in terms of the existence of
solutions to the equations vn+1=Anvn+fn in lp spaces (1≤p<∞). Then we apply the results to study the robustness of exponential dichotomy of difference equations.