Necessary and sufficient conditions for solvability of the Hartman-Wintner problem for difference equations.

The equation[image omitted] is viewed as a perturbation of the equation[image omitted] which does not oscillate at infinity. The sequences [image omitted] [image omitted] are assumed real, rn>0 for all n ≥ 0, the sequences [image omitted] may be complex-valued. We study the Hartman-Wintner problem on asymptotic 'integration' of (1) for large n in terms of solutions of (2) and the perturbation [image omitted] . [ABSTRACT FROM AUTHOR]