TY - JOUR
T1 - Nonoscillation and exponential stability of delay differential equations with oscillating coefficients
AU - Berezansky, L.
AU - Braverman, E.
N1 - Funding Information:
2000 Mathematics Subject Classification. 34K11, 34K20. Key words and phrases. Linear delay equations, exponential stability, positive fundamental function, oscillating coefficients. The first author was partially supported by Israeli Ministry of Absorption. The second author was partially supported by the NSERC Research Grant and the AIF Research Grant.
PY - 2009/1/14
Y1 - 2009/1/14
N2 - We prove that under some additional conditions, the nonoscillation of the scalar delay differential equation ẋ(t) + ∑ k=1 m a k (t)x(h k(t)) = 0 implies the exponential stability. New nonoscillation conditions are obtained for equations with positive and negative coefficients and for equations of arbitrary signs. As an example, we present an exponentially stable equation with two delays and two oscillating coefficients.
AB - We prove that under some additional conditions, the nonoscillation of the scalar delay differential equation ẋ(t) + ∑ k=1 m a k (t)x(h k(t)) = 0 implies the exponential stability. New nonoscillation conditions are obtained for equations with positive and negative coefficients and for equations of arbitrary signs. As an example, we present an exponentially stable equation with two delays and two oscillating coefficients.
KW - Exponential stability
KW - Linear delay equations
KW - Oscillating coefficients
KW - Positive fundamental function
UR - http://www.scopus.com/inward/record.url?scp=59449105131&partnerID=8YFLogxK
U2 - 10.1007/s10883-008-9058-4
DO - 10.1007/s10883-008-9058-4
M3 - Article
AN - SCOPUS:59449105131
SN - 1079-2724
VL - 15
SP - 63
EP - 82
JO - Journal of Dynamical and Control Systems
JF - Journal of Dynamical and Control Systems
IS - 1
ER -