On the delay differential equation y'(x) = ay(τ(x)) + by(x)

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Department of Mathematics Technical University of Brno Technická 2 61669 Brno, Czech Republic

The paper discusses the asymptotic properties of solutions of the scalar functional differential equation

y' (x) = a y (τ (x)) + b y (x), x \in [x_{0}, \infty]

. Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.

functional differential equation, functional (nondifferential) equation, asymptotic behaviour

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1991 Mathematics Subject Classification: Primary 34K15, 34K25; Secondary 39B05.