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On exponential dichotomy for linear difference equations with bounded and unbounded delay. (English) Zbl 1127.39007

Agarwal, Ravi P. (ed.) et al., Proceedings of the international conference on differential and difference equations and their applications, Melbourne, FL, USA, August 1–5, 2005. New York: Hindawi Publishing Corporation (ISBN 977-5945-38-0/hbk). 169-178 (2006).
Summary: We consider the exponential dichotomy for solutions of a linear delay difference equation in a Banach space. If the delay is bounded, then the equivalence of the dichotomy in the delay and nondelay cases is demonstrated, with further application of some recently obtained results for nondelay difference equations. In the case, when the delay is not bounded, but there is a certain memory decay in coefficients, the exponential dichotomy of solutions is also proved.
For the entire collection see [Zbl 1118.34001].

MSC:

39A11 Stability of difference equations (MSC2000)
39A70 Difference operators
47B39 Linear difference operators
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