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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Asymptotic behavior of a linear delay difference equation

Authors: R. D. Driver, G. Ladas and P. N. Vlahos
Journal: Proc. Amer. Math. Soc. 115 (1992), 105-112
MSC: Primary 39A12; Secondary 34K25
MathSciNet review: 1111217
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Abstract: Consider the linear delay difference equations

$\displaystyle {x_{n + 1}} - {x_n} = \sum\limits_{j = 1}^m {{a_j}({x_{n - {k_j}}} - {x_{n - {l_j}}}),\quad n = 0,1,2, \ldots } $


$\displaystyle {y_{n + 1}} - {y_n} = \sum\limits_{j = 1}^k {{b_j}{y_{n - j}},\quad n = 0,1,2, \ldots ,} $

where the coefficients $ {a_j}$ and $ {b_j}$ are real and $ {k_j}$ and $ {l_j}$ are nonnegative integers. In this note we describe, in terms of the initial conditions, the asymptotic behavior of solutions of these equations in several cases when the characteristic equation has a dominant real root. Some of the results extend to systems of equations.

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Article copyright: © Copyright 1992 American Mathematical Society