Asymptotic formulas for a scalar linear delay differential equation
The linear delay differential equation $$ x'(t)=p(t)x(t-r) $$ is considered, where $r>0$ and the coefficient $p:[t_0,\infty)\to\mathbb{R}$ is a continuous function such that $p(t)\to0$ as $t\to\infty$. In a recent paper [M. Pituk, G. Röst, Bound. Value Probl. 2014:114] an asymptotic descript...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
University of Szeged
2016-09-01
|
Series: | Electronic Journal of Qualitative Theory of Differential Equations |
Subjects: | |
Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4770 |
id |
doaj-b1c7601843274f10b270956ea8f71cbc |
---|---|
record_format |
Article |
spelling |
doaj-b1c7601843274f10b270956ea8f71cbc2021-07-14T07:21:28ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752016-09-0120167211410.14232/ejqtde.2016.1.724770Asymptotic formulas for a scalar linear delay differential equationIstván Győri0Mihály Pituk1Department of Mathematics and Computing, University of Pannonia, Veszprém, HungaryUniversity of Pannonia, Veszprém, Hungary The linear delay differential equation $$ x'(t)=p(t)x(t-r) $$ is considered, where $r>0$ and the coefficient $p:[t_0,\infty)\to\mathbb{R}$ is a continuous function such that $p(t)\to0$ as $t\to\infty$. In a recent paper [M. Pituk, G. Röst, Bound. Value Probl. 2014:114] an asymptotic description of the solutions has been given in terms of a special solution of the associated formal adjoint equation and the initial data. In this paper, we give a representation of the special solution of the formal adjoint equation. Under some additional conditions, the representation theorem yields explicit asymptotic formulas for the solutions as $t\to\infty$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4770delay differential equationformal adjoint equationasymptotic formulas |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
István Győri Mihály Pituk |
spellingShingle |
István Győri Mihály Pituk Asymptotic formulas for a scalar linear delay differential equation Electronic Journal of Qualitative Theory of Differential Equations delay differential equation formal adjoint equation asymptotic formulas |
author_facet |
István Győri Mihály Pituk |
author_sort |
István Győri |
title |
Asymptotic formulas for a scalar linear delay differential equation |
title_short |
Asymptotic formulas for a scalar linear delay differential equation |
title_full |
Asymptotic formulas for a scalar linear delay differential equation |
title_fullStr |
Asymptotic formulas for a scalar linear delay differential equation |
title_full_unstemmed |
Asymptotic formulas for a scalar linear delay differential equation |
title_sort |
asymptotic formulas for a scalar linear delay differential equation |
publisher |
University of Szeged |
series |
Electronic Journal of Qualitative Theory of Differential Equations |
issn |
1417-3875 1417-3875 |
publishDate |
2016-09-01 |
description |
The linear delay differential equation
$$
x'(t)=p(t)x(t-r)
$$
is considered, where $r>0$ and the coefficient $p:[t_0,\infty)\to\mathbb{R}$ is a continuous function such that $p(t)\to0$ as $t\to\infty$. In a recent paper [M. Pituk, G. Röst, Bound. Value Probl. 2014:114] an asymptotic description of the solutions has been given in terms of a special solution of the associated formal adjoint equation and the initial data. In this paper, we give a representation of the special solution of the formal adjoint equation. Under some additional conditions, the representation theorem yields explicit asymptotic formulas for the solutions as $t\to\infty$. |
topic |
delay differential equation formal adjoint equation asymptotic formulas |
url |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4770 |
work_keys_str_mv |
AT istvangyori asymptoticformulasforascalarlineardelaydifferentialequation AT mihalypituk asymptoticformulasforascalarlineardelaydifferentialequation |
_version_ |
1721303630082998272 |