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ASYMPTOTIC ESTIMATION FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH SEVERAL
DELAYS

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*Jan Cermák*

**Address.** Department of Mathematics, Technical University of Brno,
Technická 2, 616 69 Brno, CZECH REPUBLIC
**E-mail:** cermakh@mat.fme.vutbr.cz

**Abstract.** We discuss the asymptotic behaviour of all solutions
of the functional differential equation $$y'(x)=\dsize\sum_{i=1}^ma_i(x)y(\tau_i(x))+b(x)y(x)\,,$$
where $b(x)<0$. The asymptotic bounds are given in terms of a solution
of the functional nondifferential equation $$\dsize\sum_{i=1}^m|a_i(x)|\omega
(\tau_i(x))+b(x)\omega (x)=0.$$

**AMSclassification.** 34K15, 34K25; Secondary 39B99

**Keywords.** Functional differential equation, functional nondifferential
equation, asymptotic behaviour, transformation