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.