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On exponential stability of linear differential equations with several delays. (English) Zbl 1112.34055

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

x ˙(t)+ k=1 m a k (t)x(h k (t))=0,(*)

with k=1 m a k (t)0, h k (t)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.

34K20Stability theory of functional-differential equations
34K06Linear functional-differential equations