On the critical case in oscillation for differential equations with a single delay and with several delays

Leonid Berezansky; Jaromír Baštinec; Josef Diblík; Zdeněk Šmarda

doi:10.1155/2010/417869

On the critical case in oscillation for differential equations with a single delay and with several delays

Leonid Berezansky
, Jaromír Baštinec
, Josef Diblík
, Zdeněk Šmarda

Department of Mathematics

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

22 Scopus citations

Abstract

New nonoscillation and oscillation criteria are derived for scalar delay differential equations x(t)+a(t)x(h(t))=0,a(t)≥0,h(t)≤t,t≥ t 0, and x(t)+ Σ_k=1^m a_k(t)x(h_k(t))=0, a_k(t)≥0, h_k(t)≤t, and t≥ t ₀, in the critical case including equations with several unbounded delays, without the usual assumption that the parameters a, h, a_k, and h_k of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations.

Original language	English
Article number	417869
Journal	Abstract and Applied Analysis
Volume	2010
DOIs	https://doi.org/10.1155/2010/417869
State	Published - 22 Nov 2010

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "On the critical case in oscillation for differential equations with a single delay and with several delays",

abstract = "New nonoscillation and oscillation criteria are derived for scalar delay differential equations x(t)+a(t)x(h(t))=0,a(t)≥0,h(t)≤t,t≥ t 0, and x(t)+ Σk=1m ak(t)x(hk(t))=0, ak(t)≥0, hk(t)≤t, and t≥ t 0, in the critical case including equations with several unbounded delays, without the usual assumption that the parameters a, h, ak, and hk of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations.",

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T1 - On the critical case in oscillation for differential equations with a single delay and with several delays

AU - Berezansky, Leonid

AU - Baštinec, Jaromír

AU - Diblík, Josef

AU - Šmarda, Zdeněk

PY - 2010/11/22

Y1 - 2010/11/22

N2 - New nonoscillation and oscillation criteria are derived for scalar delay differential equations x(t)+a(t)x(h(t))=0,a(t)≥0,h(t)≤t,t≥ t 0, and x(t)+ Σk=1m ak(t)x(hk(t))=0, ak(t)≥0, hk(t)≤t, and t≥ t 0, in the critical case including equations with several unbounded delays, without the usual assumption that the parameters a, h, ak, and hk of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations.

AB - New nonoscillation and oscillation criteria are derived for scalar delay differential equations x(t)+a(t)x(h(t))=0,a(t)≥0,h(t)≤t,t≥ t 0, and x(t)+ Σk=1m ak(t)x(hk(t))=0, ak(t)≥0, hk(t)≤t, and t≥ t 0, in the critical case including equations with several unbounded delays, without the usual assumption that the parameters a, h, ak, and hk of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations.

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DO - 10.1155/2010/417869

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VL - 2010

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

M1 - 417869

ER -

On the critical case in oscillation for differential equations with a single delay and with several delays

Abstract

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