*(English)*Zbl 1112.34055

Studied in this paper is the exponential stability of the following nonautonomous delayed linear equation

with ${\sum}_{k=1}^{m}{a}_{k}\left(t\right)\ge 0$, ${h}_{k}\left(t\right)\le t$. Applying the comparison method based on a Bohl-Perron-type theorem, the authors obtain some new stability conditions on exponential stability of ($*$). These conditions are in “iterative” and “limit” forms. The results are compared with some existing ones by several examples. The study is a continuation of the paper of the authors [J. Math. Anal. Appl. 314, No. 2, 391–411 (2006; Zbl 1101.34057)], where ordinary differential equations are applied as comparison equations, while in this paper under review delay differential equations with positive coefficients and a positive fundamental function are used for comparison.

##### MSC:

34K20 | Stability theory of functional-differential equations |

34K06 | Linear functional-differential equations |