Linearized oscillation theory for a nonlinear nonautonomous delay differential equation

Leonid Berezansky; Elena Braverman

doi:10.1016/S0377-0427(02)00741-0

Linearized oscillation theory for a nonlinear nonautonomous delay differential equation

Leonid Berezansky, Elena Braverman

Department of Mathematics

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

14 Scopus citations

Abstract

Oscillation properties of two following equations are compared: a scalar nonlinear delay differential equation y(t) + ∑_k=1 r_k(t) f_k[y(h_k(t))] = 0 with r_k(t) ≥ 0, h_k(t) ≤ t, and a linear delay differential equation x(t) + ∑_k=1^m r_k(t)x(t)) = 0. Coefficients r_k(t) and delays are not assumed to be continuous. As an application, explicit oscillation and nonoscillation conditions are established for nonlinear equations arising in population dynamics.

Original language	English
Pages (from-to)	119-127
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	151
Issue number	1
DOIs	https://doi.org/10.1016/S0377-0427(02)00741-0
State	Published - 1 Feb 2003

Keywords

Equations of population dynamics
Linearized theory
Nonoscillation
Oscillation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0377-0427(02)00741-0

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title = "Linearized oscillation theory for a nonlinear nonautonomous delay differential equation",

abstract = "Oscillation properties of two following equations are compared: a scalar nonlinear delay differential equation y(t) + ∑k=1 rk(t) fk[y(hk(t))] = 0 with rk(t) ≥ 0, hk(t) ≤ t, and a linear delay differential equation x(t) + ∑k=1m rk(t)x(t)) = 0. Coefficients rk(t) and delays are not assumed to be continuous. As an application, explicit oscillation and nonoscillation conditions are established for nonlinear equations arising in population dynamics.",

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author = "Leonid Berezansky and Elena Braverman",

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T1 - Linearized oscillation theory for a nonlinear nonautonomous delay differential equation

AU - Berezansky, Leonid

AU - Braverman, Elena

PY - 2003/2/1

Y1 - 2003/2/1

N2 - Oscillation properties of two following equations are compared: a scalar nonlinear delay differential equation y(t) + ∑k=1 rk(t) fk[y(hk(t))] = 0 with rk(t) ≥ 0, hk(t) ≤ t, and a linear delay differential equation x(t) + ∑k=1m rk(t)x(t)) = 0. Coefficients rk(t) and delays are not assumed to be continuous. As an application, explicit oscillation and nonoscillation conditions are established for nonlinear equations arising in population dynamics.

AB - Oscillation properties of two following equations are compared: a scalar nonlinear delay differential equation y(t) + ∑k=1 rk(t) fk[y(hk(t))] = 0 with rk(t) ≥ 0, hk(t) ≤ t, and a linear delay differential equation x(t) + ∑k=1m rk(t)x(t)) = 0. Coefficients rk(t) and delays are not assumed to be continuous. As an application, explicit oscillation and nonoscillation conditions are established for nonlinear equations arising in population dynamics.

KW - Equations of population dynamics

KW - Linearized theory

KW - Nonoscillation

KW - Oscillation

UR - http://www.scopus.com/inward/record.url?scp=0037294683&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(02)00741-0

DO - 10.1016/S0377-0427(02)00741-0

M3 - Article

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SN - 0377-0427

VL - 151

SP - 119

EP - 127

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Linearized oscillation theory for a nonlinear nonautonomous delay differential equation

Abstract

Keywords

ASJC Scopus subject areas

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