Exponential dichotomy of difference equations in <it>l</it><sub><it>p</it></sub>-phase spaces on the half-line

<p/> <p>For a sequence of bounded linear operators <inline-formula><graphic file="1687-1847-2006-058453-i1.gif"/></inline-formula> on a Banach space <it>X</it>, we investigate the characterization of exponential dichotomy of the difference equation...

Full description

Bibliographic Details
Main Authors: Huy Nguyen Thieu, Ha Vu Thi Ngoc
Format: Article
Language:English
Published: SpringerOpen 2006-01-01
Series:Advances in Difference Equations
Online Access:http://www.advancesindifferenceequations.com/content/2006/058453
Description
Summary:<p/> <p>For a sequence of bounded linear operators <inline-formula><graphic file="1687-1847-2006-058453-i1.gif"/></inline-formula> on a Banach space <it>X</it>, we investigate the characterization of exponential dichotomy of the difference equations <it>v</it><sub><it>n</it>+1</sub> = <it>A</it><sub><it>n</it></sub><it>v</it><sub><it>n</it></sub>. We characterize the exponential dichotomy of difference equations in terms of the existence of solutions to the equations <it>v</it><sub><it>n</it>+1</sub> = <it>A</it><sub><it>n</it></sub><it>v</it><sub><it>n</it></sub> + <it>f</it><sub><it>n</it></sub> in <it>l</it><sub><it>p</it></sub> spaces (1 &#8804; <it>p</it> &lt; &#8734;). Then we apply the results to study the robustness of exponential dichotomy of difference equations.</p>
ISSN:1687-1839
1687-1847