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Zbl 1112.34055
Berezansky, Leonid; Braverman, Elena
On exponential stability of linear differential equations with several delays. (English)
[J] J. Math. Anal. Appl. 324, No. 2, 1336-1355 (2006). ISSN 0022-247X

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 $\sum_{k=1}^m a_k(t)\ge 0$, $h_k(t)\le t$. 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.
[Yuming Chen (Waterloo)]

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K06 Linear functional-differential equations

Keywords: delay equation; exponential stability; positive fundamental function; Bohl-Perron-type theorem

Citations: Zbl 1101.34057

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