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.
@article{107820,
author = {Robert Hakl and Alexander Lomtatidze},
title = {A note on the Cauchy problem for first order linear differential equations with a deviating argument},
journal = {Archivum Mathematicum},
volume = {038},
year = {2002},
pages = {61-71},
zbl = {1087.34043},
mrnumber = {1899569},
language = {en},
url = {http://dml.mathdoc.fr/item/107820}
}
Hakl, Robert; Lomtatidze, Alexander. A note on the Cauchy problem for first order linear differential equations with a deviating argument. Archivum Mathematicum, Tome 038 (2002) pp. 61-71. http://gdmltest.u-ga.fr/item/107820/
A note on the Fredholm property of boundary value problems for linear functional differential equations, Mem. Differential Equations Math. Phys. 20 (2000), 133–135. | MR 1789344 | Zbl 0968.34049
Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations, Czechoslovak Math. J., to appear. | MR 1923257 | Zbl 1023.34055
New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations, Math. Bohem., to appear. | MR 1942637 | Zbl 1017.34065
On boundary value problems for systems of linear functional differential equations, Czechoslovak Math. J. 47 (1997), No. 2, 341–373. (1997) | MR 1452425 | Zbl 0930.34047