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

Robert Hakl; Alexander Lomtatidze

Archivum Mathematicum (2002)

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

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topHakl, 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 -

## References

top- Bravyi E., A note on the Fredholm property of boundary value problems for linear functional differential equations, Mem. Differential Equations Math. Phys. 20 (2000), 133–135. Zbl0968.34049MR1789344
- Bravyi E., Hakl R., Lomtatidze A., Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations, Czechoslovak Math. J., to appear. Zbl1023.34055MR1923257
- Hakl R., Lomtatidze A., Půža B., New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations, Math. Bohem., to appear. Zbl1017.34065MR1942637
- Kiguradze I., Půža B., On boundary value problems for systems of linear functional differential equations, Czechoslovak Math. J. 47 (1997), No. 2, 341–373. (1997) Zbl0930.34047MR1452425

## Citations in EuDML Documents

top- Robert Hakl, Alexander Lomtatidze, Jiří Šremr, Solvability of a periodic type boundary value problem for first order scalar functional differential equations
- Robert Hakl, Alexander Lomtatidze, Jiří Šremr, On an antiperiodic type boundary value problem for first order linear functional differential equations

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