Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 99, pp. 1-5.
Title: Stability of delay differential equations with
oscillating coefficients
Author: Michael I. Gil' (Ben Gurion Univ. of the Negev, Israel)
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.