### 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.

Original language | English |
---|---|

Article number | 67492 |

Journal | Advances in Difference Equations |

Volume | 2006 |

DOIs | |

Publication status | Published - 2007 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Algebra and Number Theory
- Analysis

### Cite this

*Advances in Difference Equations*,

*2006*, [67492]. https://doi.org/10.1155/2007/67492

**Asymptotic expansions for higher-order scalar difference equations.** / Agarwal, Ravi P.; Pituk, M.

Research output: Contribution to journal › Article

*Advances in Difference Equations*, vol. 2006, 67492. https://doi.org/10.1155/2007/67492

}

TY - JOUR

T1 - Asymptotic expansions for higher-order scalar difference equations

AU - Agarwal, Ravi P.

AU - Pituk, M.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34247328501&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247328501&partnerID=8YFLogxK

U2 - 10.1155/2007/67492

DO - 10.1155/2007/67492

M3 - Article

AN - SCOPUS:34247328501

VL - 2006

JO - Advances in Difference Equations

JF - Advances in Difference Equations

SN - 1687-1839

M1 - 67492

ER -