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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)239-246
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume400
Issue number1
DOIs
Publication statusPublished - Apr 1 2013

Fingerprint

Tauberian theorem
Real Roots
Linear Difference Equation
Continuous Solution
Large Time Behavior
Characteristic equation
Difference equations

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.

In: Journal of Mathematical Analysis and Applications, Vol. 400, No. 1, 01.04.2013, p. 239-246.

Research output: Contribution to journalArticle

@article{77aee0c5f13d4f40b608ce601fa79478,
title = "Large time behavior of a linear difference equation with rationally non-related delays",
abstract = "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.",
keywords = "Characteristic equation, Difference equation, Dominant root, Large time behavior, Rationally non-related delays",
author = "M. Pituk",
year = "2013",
month = "4",
day = "1",
doi = "10.1016/j.jmaa.2012.11.014",
language = "English",
volume = "400",
pages = "239--246",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

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 -