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  • Research Article
  • Open Access

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Advances in Difference Equations20072007:067492

https://doi.org/10.1155/2007/67492

  • Received: 26 November 2006
  • Accepted: 23 February 2007
  • Published:

Abstract

We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA
(2)
Department of Mathematics and Computing, University of Veszprém, P.O. Box 158, Veszprém, 8201, Hungary

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