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

Nguyen Thieu Huy and Vu Thi Ngoc Ha

 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

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.