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A note on the Cauchy problem for first order linear differential equations with a deviating argument. (English) Zbl 1087.34043
This paper, from a series of results successively describing the basic properties of solutions of functional differential equations, is devoted to the Cauchy problem $u'(t)=p(t)u(\tau (t))+q(t),\qquad u(a)=c,$ where $$p$$ and $$q$$ are Lebesgue integrable on $$[a,b]$$ real functions, $$c\in \mathbb R$$, and $$\tau :[a,b]\to [\tau _0,\tau _1]$$ is a measurable function. Here $$[\tau _0,\tau _1]\subseteq [a,b]$$ can be degenerated to a point.
The obtained effective criteria are in some sense nonimprovable, which is shown by several examples.

##### MSC:
 34K10 Boundary value problems for functional-differential equations
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