TY - JOUR
T1 - On exponential stability of linear differential equations with several delays
AU - Berezansky, Leonid
AU - Braverman, Elena
N1 - Funding Information:
* Corresponding author. E-mail address: [email protected] (E. Braverman). 1 Partially supported by Israeli Ministry of Absorption. 2 Partially supported by the NSERC Research Grant and the AIF Research Grant.
PY - 2006/12/15
Y1 - 2006/12/15
N2 - New explicit conditions of exponential stability are obtained for the nonautonomous linear equationover(x, ̇) (t) + underover(∑, k = 1, m) ak (t) x (hk (t)) = 0, where ∑k = 1m ak (t) ≥ 0, hk (t) ≤ t, in particular, for equations with positive and negative coefficients. We apply the comparison method based on the Bohl-Perron type theorem. Exponentially stable delay equations with a positive fundamental function are used for comparison.
AB - New explicit conditions of exponential stability are obtained for the nonautonomous linear equationover(x, ̇) (t) + underover(∑, k = 1, m) ak (t) x (hk (t)) = 0, where ∑k = 1m ak (t) ≥ 0, hk (t) ≤ t, in particular, for equations with positive and negative coefficients. We apply the comparison method based on the Bohl-Perron type theorem. Exponentially stable delay equations with a positive fundamental function are used for comparison.
KW - Delay equations
KW - Exponential stability
KW - Positive fundamental function
UR - http://www.scopus.com/inward/record.url?scp=33749506996&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2006.01.022
DO - 10.1016/j.jmaa.2006.01.022
M3 - Article
AN - SCOPUS:33749506996
SN - 0022-247X
VL - 324
SP - 1336
EP - 1355
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -