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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2006/058453 |
| 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 ≤ <it>p</it> < ∞). Then we apply the results to study the robustness of exponential dichotomy of difference equations.</p> |
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| ISSN: | 1687-1839 1687-1847 |