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
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.