Linearized oscillation theory for a nonlinear equation with a distributed delay

Leonid Berezansky; Elena Braverman

doi:10.1016/j.mcm.2007.10.003

Linearized oscillation theory for a nonlinear equation with a distributed delay

Leonid Berezansky
, Elena Braverman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We obtain linearized oscillation theorems for the equation with distributed delays (1)over(x, ̇) (t) + underover(∑, k = 1, m) r_k (t) ∫_{- ∞}^t f_k (x (s)) d_s R_k (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) r_k (t) f_k^′ (ξ_k (t))) x (g (t)) = 0 .

Original language	English
Pages (from-to)	287-304
Number of pages	18
Journal	Mathematical and Computer Modelling
Volume	48
Issue number	1-2
DOIs	https://doi.org/10.1016/j.mcm.2007.10.003
State	Published - 1 Jul 2008

Keywords

Distributed delay
Lasota-Wazewska model
Linearization
Logistic equation
Nicholson's blowflies equation
Oscillation

ASJC Scopus subject areas

Modeling and Simulation
Computer Science Applications

Access to Document

10.1016/j.mcm.2007.10.003

Cite this

@article{3bb0004360a44b47867b9cc51fc64092,

title = "Linearized oscillation theory for a nonlinear equation with a distributed delay",

abstract = "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 .",

keywords = "Distributed delay, Lasota-Wazewska model, Linearization, Logistic equation, Nicholson's blowflies equation, Oscillation",

author = "Leonid Berezansky and Elena Braverman",

year = "2008",

month = jul,

day = "1",

doi = "10.1016/j.mcm.2007.10.003",

language = "English",

volume = "48",

pages = "287--304",

journal = "Mathematical and Computer Modelling",

issn = "0895-7177",

publisher = "Elsevier Ltd.",

number = "1-2",

}

TY - JOUR

T1 - Linearized oscillation theory for a nonlinear equation with a distributed delay

AU - Berezansky, Leonid

AU - Braverman, Elena

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 - https://www.scopus.com/pages/publications/43449112941

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 -

Linearized oscillation theory for a nonlinear equation with a distributed delay

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this