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Zbl 1187.34096
Berezansky, Leonid; Braverman, Elena
On exponential stability of a linear delay differential equation with an oscillating coefficient.
(English)
[J] Appl. Math. Lett. 22, No. 12, 1833-1837 (2009). ISSN 0893-9659

Summary: New explicit exponential stability conditions are obtained for the nonautonomous linear equation $$\dot x (t) = a(t)x(h(t))=0,$$ where $h(t) \leq t$ and $a(t)$ is an oscillating function. We apply the comparison method based on the Bohl-Perron type theorem. Coefficients and delays are not assumed to be continuous. Some real-world applications and several examples are also discussed.
MSC 2000:
*34K20 Stability theory of functional-differential equations
34K06 Linear functional-differential equations

Keywords: delay equations; exponential stability; oscillating coefficient; Bohl-Perron type theorem

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