Consider the nonhomogeneous Linear recurrence system x(n+1) = (A + B-n)x(n) + g(n), where A and B-n (n = 0, 1,...) are square matrices and g(n) (n = 0, 1....) are column vectors. In this paper, we describe, in terms of the initial condition, the asymptotic behavior of the solutions of this equation in the case when A has a simple dominant eigenvalue lambda(0), Sigma(n=0)(infinity) parallel toB(n)parallel to < infinity and Sigma(n=0)(infinity) lambda(0)(-n)parallel tog(n)parallel to < infinity. The proof is based on the duality between the solutions of the above equation and the solutions of the associated adjoint equation. As a consequence, we obtain a similar result for higher order scalar equations. (C) 2002 Elsevier Science (USA). [References: 28]
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