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In this paper, we describe the asymptotic behavior of the solutions of the difference equation provided that the characteristic equation of the corresponding equation with constant coefficients has a dominant root and the sequences are in l 2 and of bounded variation. The main tools in the proof are perturbation theorems on asymptotic constancy and stability of the solutions, decomposition in the variation-of-constants formula and estimates on the complementary spaces.
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Mihály Pituk (1997) studied this question.
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