Oscillation properties of a logistic equation with distributed delay

Leonid Berezansky; Elena Braverman

doi:10.1016/S1468-1218(02)00010-X

Oscillation properties of a logistic equation with distributed delay

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

23 Scopus citations

Abstract

For a scalar delay logistic equation ̇y(t) = y(t) ∑_i=1^m r_i(t) (1 - 1/K ∫_-∞^t y(s)d_sR_i(t,s)) the oscillation properties are established, which are well known for a linear delay differential equation, such as comparison theorems, explicit oscillation conditions, dependence of the solution sign on the initial function and the initial value. Explicit oscillation and nonoscillation conditions are presented and compared to the known ones.

Original language	English
Pages (from-to)	1-19
Number of pages	19
Journal	Nonlinear Analysis: Real World Applications
Volume	4
Issue number	1
DOIs	https://doi.org/10.1016/S1468-1218(02)00010-X
State	Published - 1 Mar 2003

Keywords

Comparison theorems
Distributed delays
Logistic equation
Nonoscillation
Oscillation

ASJC Scopus subject areas

Analysis
General Engineering
General Economics, Econometrics and Finance
Computational Mathematics
Applied Mathematics

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10.1016/S1468-1218(02)00010-X

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abstract = "For a scalar delay logistic equation{\. }y(t) = y(t) ∑i=1m ri(t) (1 - 1/K ∫-∞t y(s)dsRi(t,s)) the oscillation properties are established, which are well known for a linear delay differential equation, such as comparison theorems, explicit oscillation conditions, dependence of the solution sign on the initial function and the initial value. Explicit oscillation and nonoscillation conditions are presented and compared to the known ones.",

keywords = "Comparison theorems, Distributed delays, Logistic equation, Nonoscillation, Oscillation",

author = "Leonid Berezansky and Elena Braverman",

note = "Funding Information: This research was partially supported by Israel Ministry of Absorption. The authors are very grateful to the referee for remarks which helped to improve the paper.",

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AU - Berezansky, Leonid

AU - Braverman, Elena

N1 - Funding Information: This research was partially supported by Israel Ministry of Absorption. The authors are very grateful to the referee for remarks which helped to improve the paper.

PY - 2003/3/1

Y1 - 2003/3/1

N2 - For a scalar delay logistic equation ̇y(t) = y(t) ∑i=1m ri(t) (1 - 1/K ∫-∞t y(s)dsRi(t,s)) the oscillation properties are established, which are well known for a linear delay differential equation, such as comparison theorems, explicit oscillation conditions, dependence of the solution sign on the initial function and the initial value. Explicit oscillation and nonoscillation conditions are presented and compared to the known ones.

AB - For a scalar delay logistic equation ̇y(t) = y(t) ∑i=1m ri(t) (1 - 1/K ∫-∞t y(s)dsRi(t,s)) the oscillation properties are established, which are well known for a linear delay differential equation, such as comparison theorems, explicit oscillation conditions, dependence of the solution sign on the initial function and the initial value. Explicit oscillation and nonoscillation conditions are presented and compared to the known ones.

KW - Comparison theorems

KW - Distributed delays

KW - Logistic equation

KW - Nonoscillation

KW - Oscillation

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JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 1

ER -

Oscillation properties of a logistic equation with distributed delay

Abstract

Keywords

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