TY - JOUR
T1 - Linearized oscillation theory for a nonlinear equation with a distributed delay
AU - Berezansky, Leonid
AU - Braverman, Elena
N1 - Funding Information:
The first author was partially supported by the Israeli Ministry of Absorption. The second author was partially supported by the NSERC Research Grant and the AIF Research Grant. The authors are grateful to the editor for valuable comments on the presentation of the paper.
PY - 2008/7/1
Y1 - 2008/7/1
N2 - We obtain linearized oscillation theorems for the equation with distributed delays (1)over(x, ̇) (t) + underover(∑, k = 1, m) rk (t) ∫- ∞t fk (x (s)) ds Rk (t, s) = 0 . The results are applied to logistic, Lasota-Wazewska and Nicholson's blowflies equations with a distributed delay. In addition, the "Mean Value Theorem" is proved which claims that a solution of (1) also satisfies the linear equation with a variable concentrated delay over(x, ̇) (t) + (underover(∑, k = 1, m) rk (t) fk′ (ξk (t))) x (g (t)) = 0 .
AB - We obtain linearized oscillation theorems for the equation with distributed delays (1)over(x, ̇) (t) + underover(∑, k = 1, m) rk (t) ∫- ∞t fk (x (s)) ds Rk (t, s) = 0 . The results are applied to logistic, Lasota-Wazewska and Nicholson's blowflies equations with a distributed delay. In addition, the "Mean Value Theorem" is proved which claims that a solution of (1) also satisfies the linear equation with a variable concentrated delay over(x, ̇) (t) + (underover(∑, k = 1, m) rk (t) fk′ (ξk (t))) x (g (t)) = 0 .
KW - Distributed delay
KW - Lasota-Wazewska model
KW - Linearization
KW - Logistic equation
KW - Nicholson's blowflies equation
KW - Oscillation
UR - http://www.scopus.com/inward/record.url?scp=43449112941&partnerID=8YFLogxK
U2 - 10.1016/j.mcm.2007.10.003
DO - 10.1016/j.mcm.2007.10.003
M3 - Article
AN - SCOPUS:43449112941
SN - 0895-7177
VL - 48
SP - 287
EP - 304
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
IS - 1-2
ER -