Linear differential equations with several unbounded delays

Jan Cermak

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


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.