We offer
several perspectives on the behavior at infinity of solutions of
discrete Schroedinger equations. First we study pairs of discrete
Schroedinger equations whose potential functions differ by a quantity
that can be considered small in a suitable sense as the index n
\rightarrow \infty. With simple assumptions on the growth rate of the
solutions of the original system, we show that the perturbed system has a
fundamental set of solutions with the same behavior at infinity,
employing a variation-of-constants scheme to produce a convergent
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