Asymptotic expansions for higher-order scalar difference equations

Ravi P. Agarwal, Mihály Pituk

Research output: Article

10 Citations (Scopus)


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.

Original languageEnglish
Article number67492
JournalAdvances in Difference Equations
Publication statusPublished - ápr. 27 2007

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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