Asymptotic properties of solutions to nonautonomous Volterra difference systems with infinite delay. (English) Zbl 1002.39007

Cuevas, C.; Pinto, M.

Comput. Math. Appl. 42, No. 3-5, 671-685 (2001).

The authors show that under certain conditions there is a one-to-one correspondence between weighted bounded solutions of a linear nonautonomous Volterra difference system with infinite delay and its perturbed system. Under additional assumptions, this correspondence is elevated to asymptotic equivalence. On the other side, the authors prove the existence of weighted convergent solutions.

Reviewer: Wang-Tong Li (Lanzhou)

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

perturbation; weighted bounded solutions; linear nonautonomous Volterra difference system with infinite delay; asymptotic equivalence; weighted convergent solutions

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