Explicit integral criteria for the existence of positive solutions of the linear delayed equation $\dot x(t) =-c(t)x(t-\tau(t))$

Druh výsledku
článek v časopise ve Web of Science, Jimp

The paper analyses the linear differential equation with single delay $\dot x(t)=-c(t)x(t-\tau(t))$ with continuous $\tau\colon [t_0,\infty)\to (0,r]$, $r>0$, $t_0\in \bR$, and $c\colon [t_0-r,\infty)\to (0,\infty)$. New explicit integral criteria for the existence of a positive solution expressed in terms of $c$ and $\tau$ are derived, an overview of known relevant criteria is provided, and relevant comparisons are also given. It is demonstrated that the known criteria are consequences of the new results.

Klíčová slova
time delay, linear differential equation, positive solution, integral criterion