Об асимптотическом поведении решений одного класса дифференциально-разностных уравнений

Abstract

The forced delay differential equation $\dot x(t)=a(t)x(t-\omega),\ t\in\R_{+}$ with complex coefficient $a(t)$ satisfying the condition $a(t+\omega)=Ma(t)$, $M\in\C$, is being considered. Effective sufficient conditions for asymptotic behaviour of solutions were obtained, in particular, the conditions for solutions' boundedness, convergence to some constant value and unboundedness.