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