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.