Electron. J. Diff. Equ., Vol. 2010(2010), No. 99, pp. 1-5.

Stability of delay differential equations with oscillating coefficients

Michael I. Gil'

Abstract:
We study the solutions to the delay differential equation equation
$$ \dot x(t)=-a(t)x(t-h), $$
where the coefficient $a(t)$ is not necessarily positive. It is proved that this equation is exponentially stable provided that $a(t)=b+c(t)$ for some positive constant b less than $\pi/(2h)$, and the integral $\int_0^t c(s)ds$ is sufficiently small for all $t>0$. In this case the 3/2-stability theorem is improved.

Submitted April 13, 2010. Published July 22, 2010.
Math Subject Classifications: 34K20.
Key Words: Linear delay differential equation; exponential stability.

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Michael I. Gil'
Department of Mathematics
Ben Gurion University of the Negev
P.0. Box 653, Beer-Sheva 84105, Israel
email: gilmi@cs.bgu.ac.il

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