Exponential dichotomy and boundedness for retarded functional difference equations

Abstract

We characterize the exponential dichotomy of difference equations with infinite delay. We apply the results to study the robustness of exponential dichotomy. This kind of dichotomy gives us relevant information about boundedness of solutions for several perturbed quasi linear systems with infinite delay. Applications to Volterra difference equations are shown.

Keywords:

• exponential dichotomy
• difference equations
• infinite delay
• robustness
• boundedness
• Volterra difference equations

Acknowledgements

The authors are grateful to the referees for pointing out omissions and misprints, and demanding vigorously details and clarifications. The second author is partially supported by CNPQ/Brazil under Grant 300068/2005-0.

Notes

1. The authors were partially supported by CNPq/Brazil.

Additional information

Notes on contributors

Fernando Cardoso

1

Claudio Cuevas

1