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

VL - 48

SP - 287

EP - 304

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 1-2

ER -