On exponential stability of linear differential equations with several delays (Q852849)

Studied in this paper is the exponential stability of the following nonautonomous delayed linear equation \[ \dot{x}(t)+\sum\limits_{k=1}^m a_k(t)x(h_k(t))=0, \tag{*} \] with \(\sum_{k=1}^m a_k(t)\geq 0\), \(h_k(t)\leq t\). Applying the comparison method based on a Bohl-Perron-type theorem, the authors obtain some new stability conditions on exponential stability of (\(\ast\)). 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.