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Zbl 1118.34069
Berezansky, Leonid; Braverman, Elena
Explicit exponential stability conditions for linear differential equations with several delays.
(English)
[J] J. Math. Anal. Appl. 332, No. 1, 246-264 (2007). ISSN 0022-247X

Summary: New explicit conditions of exponential stability are obtained for the nonautonomous linear equation $$\dot x(t)+\sum^m_{k=1}a_k(t)x (h_k(t))=0,$$ where $\sum^m_{k=1}a_k(t)\ge 0$, $h_k(t)\le t$, by comparing this equation with a nonoscillatory exponentially stable equation of the form $$\dot x(t)+\sum_{k\in I}a_k(t)x(g_k(t))=0,$$ where $I\subset\{1,\dots,m\}$, $g_k(t)\le t$. Every comparison result gives $2^m-1$ different stability conditions due to the a priori choice of a subset $I$.
MSC 2000:
*34K20 Stability theory of functional-differential equations
34K06 Linear functional-differential equations

Keywords: delay equations; positive fundamental function

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