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Linear differential equations with several unbounded delays

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*Jan Cermak*

**Address.** Dept. of Math., Faculty of Mechanical Engineering, Brno
University of Technology, Technicka 2, 616 69 Brno,

Czech Republic

**E-mail:** cermakh@mat.fme.vutbr.cz

**Abstract.** The paper is concerned with the asymptotic estimate
of the solutions of the delay differential equation $$ \dot{x}(t)=-a(t)x(t)+b_1(t)x(\tau_1(t))+b_2(t)x(\tau_2(t))
$$ with the continuous coefficients $a(t),\,b_1(t),\,b_2(t)$ and the unbounded
lags. We derive the conditions under which each solution of this equation
can be estimated in the terms of a solution of the system of Schr\" oder's
functional equations.

**AMSclassification.** 34K25, 39B22

**Keywords.** Delay differential equation, functional equation,asymptotic
behaviour of the solutions.