# A note on the Cauchy problem for first order linear differential equations with a deviating argument

Archivum Mathematicum (2002)

• Volume: 038, Issue: 1, page 61-71
• ISSN: 0044-8753

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## Abstract

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Conditions for the existence and uniqueness of a solution of the Cauchy problem ${u}^{\text{'}}\left(t\right)=p\left(t\right)u\left(\tau \left(t\right)\right)+q\left(t\right)\phantom{\rule{0.166667em}{0ex}},\phantom{\rule{2.0em}{0ex}}u\left(a\right)=c\phantom{\rule{0.166667em}{0ex}},$ established in [2], are formulated more precisely and refined for the special case, where the function $\tau$ maps the interval $\right]a,b\left[$ into some subinterval $\left[{\tau }_{0},{\tau }_{1}\right]\subseteq \left[a,b\right]$, which can be degenerated to a point.

## How to cite

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Hakl, Robert, and Lomtatidze, Alexander. "A note on the Cauchy problem for first order linear differential equations with a deviating argument." Archivum Mathematicum 038.1 (2002): 61-71. <http://eudml.org/doc/248938>.

@article{Hakl2002,
abstract = {Conditions for the existence and uniqueness of a solution of the Cauchy problem $u^\{\prime \}(t)=p(t)u(\tau (t))+q(t)\,,\qquad u(a)=c\,,$ established in [2], are formulated more precisely and refined for the special case, where the function $\tau$ maps the interval $]a,b[$ into some subinterval $[\tau _0,\tau _1]\subseteq [a,b]$, which can be degenerated to a point.},
author = {Hakl, Robert, Lomtatidze, Alexander},
journal = {Archivum Mathematicum},
keywords = {first order equation; differential equation with deviating arguments; initial value problems; first order equation; differential equation with deviating arguments; initial value problems},
language = {eng},
number = {1},
pages = {61-71},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A note on the Cauchy problem for first order linear differential equations with a deviating argument},
url = {http://eudml.org/doc/248938},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Hakl, Robert
AU - Lomtatidze, Alexander
TI - A note on the Cauchy problem for first order linear differential equations with a deviating argument
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 1
SP - 61
EP - 71
AB - Conditions for the existence and uniqueness of a solution of the Cauchy problem $u^{\prime }(t)=p(t)u(\tau (t))+q(t)\,,\qquad u(a)=c\,,$ established in [2], are formulated more precisely and refined for the special case, where the function $\tau$ maps the interval $]a,b[$ into some subinterval $[\tau _0,\tau _1]\subseteq [a,b]$, which can be degenerated to a point.
LA - eng
KW - first order equation; differential equation with deviating arguments; initial value problems; first order equation; differential equation with deviating arguments; initial value problems
UR - http://eudml.org/doc/248938
ER -

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