Abstract and Applied Analysis
Volume 2011 (2011), Article ID 178568, 19 pages
http://dx.doi.org/10.1155/2011/178568
Research Article

New Stability Conditions for Linear Differential Equations with Several Delays

Leonid Berezansky1 and Elena Braverman2

1Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
2Department of Mathematics and Statistics, University of Calgary, 2500 University Drive Northwest, Calgary, AB, Canada T2N 1N4

Received 28 January 2011; Accepted 4 April 2011

Academic Editor: Josef Diblík

Copyright © 2011 Leonid Berezansky and Elena Braverman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equation ∑ ̇ 𝑥 ( 𝑡 ) + 𝑚 𝑘 = 1 𝑎 𝑘 ( 𝑡 ) 𝑥 ( ℎ 𝑘 ( 𝑡 ) ) = 0 with measurable delays and coefficients. These results are compared to known stability tests.