Geodesic
A note on the Cauchy problem for first order linear differential equations with a deviating argument
Archivum mathematicum, Tome 38 (2002) no. 1, pp. 61-71
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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.
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.
Classification : 34K06
Keywords: first order equation; differential equation with deviating arguments; initial value problems 
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Hakl, Robert; Lomtatidze, Alexander. A note on the Cauchy problem for first order linear differential equations with a deviating argument. Archivum mathematicum, Tome 38 (2002) no. 1, pp. 61-71. http://geodesic.mathdoc.fr/item/ARM_2002_38_1_a6/

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