TY - JOUR
T1 - Explicit exponential stability conditions for linear differential equations with several delays
AU - Berezansky, Leonid
AU - Braverman, Elena
N1 - Funding Information:
* Corresponding author. E-mail address: maelena@math.ucalgary.ca (E. Braverman). 1 Partially supported by Israeli Ministry of Absorption. 2 Partially supported by the NSERC Research Grant and the AIF Research Grant.
PY - 2007/8/1
Y1 - 2007/8/1
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, by comparing this equation with a nonoscillatory exponentially stable equation of the formover(x, ̇) (t) + under(∑, k ∈ I) ak (t) x (gk (t)) = 0, where I ⊂ {1, ..., m}, gk (t) ≤ t. Every comparison result gives 2m - 1 different stability conditions due to the a priori choice of a subset I.
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, by comparing this equation with a nonoscillatory exponentially stable equation of the formover(x, ̇) (t) + under(∑, k ∈ I) ak (t) x (gk (t)) = 0, where I ⊂ {1, ..., m}, gk (t) ≤ t. Every comparison result gives 2m - 1 different stability conditions due to the a priori choice of a subset I.
KW - Delay equations
KW - Exponential stability
KW - Positive fundamental function
UR - http://www.scopus.com/inward/record.url?scp=34147170471&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2006.10.016
DO - 10.1016/j.jmaa.2006.10.016
M3 - Article
AN - SCOPUS:34147170471
VL - 332
SP - 246
EP - 264
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -