Please use this identifier to cite or link to this item:

`http://hdl.handle.net/20.500.11889/7631`

Title: | Poincaré types solutions of systems of difference equations |

Authors: | Abu-Saris, Raghib Elaydi, Saber Jang, Sophia |

Keywords: | Poincaré series;Differential equations, Partial - Solutions |

Issue Date: | 2002 |

Publisher: | Journal of Mathematical Analysis and Applications |

Abstract: | The study of asymptotics theory of ordinary difference equations originates from the work of Henry Poincar´e. In 1885, Poincar´e [19] published a seminal paper on the asymptotics of both ordinary difference and differential equations, where he studied the k th order linear nonautonomous difference equation of the form y(n + k) + (a1 + p1(n))y(n + k − 1) + · · · + (ak + pk(n))y(n) = 0 (1.1) with k ∈ Z+, ai ∈ C and pi(n) : Z+ → C for 1 ≤ i ≤ k. This equation is said to be of Poincar´e type if limn→∞ pi(n) = 0 for 1 ≤ i ≤ k. We assume that Eq.(1.1) is of Poincar´e type and associated with Eq.(1.1) its limiting equation x(n + k) + a1x(n + k − 1) + · · · + akx(n) = 0 (1.2) with the corresponding characteristic equation λ k + a1λ k−1 + · · · + ak = 0. (1.3) Suppose that λ1, λ2, ..., λk are the characteristic roots of Eq.(1.2), i.e., the roots of Eq.(1.3). It is straightforward to see that solutions of Eq.(1.2) are of the form Xr i=1 qi(n)λ n i |

URI: | http://hdl.handle.net/20.500.11889/7631 |

DOI: | 10.1016/S0022-247X(02)00239-1 |

Appears in Collections: | Fulltext Publications |

###### Files in This Item:

File | Description | Size | Format | |
---|---|---|---|---|

Poincaré types solutions of systems of difference equations.pdf | 172.65 kB | Adobe PDF | View/Open |

#### Page view(s)

118
checked on Jun 27, 2024

#### Download(s)

12
checked on Jun 27, 2024

#### Google Scholar^{TM}

Check
#### Altmetric

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.