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Asymptotic Expansions for Higher-Order Scalar Difference Equations

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.

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Correspondence to Ravi P. Agarwal.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Agarwal, R.P., Pituk, M. Asymptotic Expansions for Higher-Order Scalar Difference Equations. Adv Differ Equ 2007, 067492 (2007). https://doi.org/10.1155/2007/67492

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Keywords

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