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.

Show me the PDF file (171 KB), TEX file, and other files for this article.

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

Return to the EJDE web page