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  • Research Article
  • Open Access

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Advances in Difference Equations20072007:067492

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


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.


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


Authors’ Affiliations

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


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