### Abstract

We consider the linear difference equation x(t)=∑j=1Najx(t-rj),t≥0, where a_{j}>0, 1≤j≤N, and the delays 012N are not rationally related in the sense that r_{j}/r_{k} is irrational for some j andk. It is shown that the large time behavior of the continuous solutions can be described in terms of the unique real root of the associated characteristic equation. The proof is based on Newman's Tauberian theorem.

Original language | English |
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Pages (from-to) | 239-246 |

Number of pages | 8 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 400 |

Issue number | 1 |

DOIs | |

Publication status | Published - Apr 1 2013 |

### Fingerprint

### Keywords

- Characteristic equation
- Difference equation
- Dominant root
- Large time behavior
- Rationally non-related delays

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Large time behavior of a linear difference equation with rationally non-related delays.** / Pituk, M.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Large time behavior of a linear difference equation with rationally non-related delays

AU - Pituk, M.

PY - 2013/4/1

Y1 - 2013/4/1

N2 - We consider the linear difference equation x(t)=∑j=1Najx(t-rj),t≥0, where aj>0, 1≤j≤N, and the delays 012N are not rationally related in the sense that rj/rk is irrational for some j andk. It is shown that the large time behavior of the continuous solutions can be described in terms of the unique real root of the associated characteristic equation. The proof is based on Newman's Tauberian theorem.

AB - We consider the linear difference equation x(t)=∑j=1Najx(t-rj),t≥0, where aj>0, 1≤j≤N, and the delays 012N are not rationally related in the sense that rj/rk is irrational for some j andk. It is shown that the large time behavior of the continuous solutions can be described in terms of the unique real root of the associated characteristic equation. The proof is based on Newman's Tauberian theorem.

KW - Characteristic equation

KW - Difference equation

KW - Dominant root

KW - Large time behavior

KW - Rationally non-related delays

UR - http://www.scopus.com/inward/record.url?scp=84871708745&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871708745&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2012.11.014

DO - 10.1016/j.jmaa.2012.11.014

M3 - Article

AN - SCOPUS:84871708745

VL - 400

SP - 239

EP - 246

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -