Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II

Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II

We study the oscillation of solutions to the differential equation $$ dot{x}(t) +a_1(t)x[r(t)]+a_2(t)x[p(t)]=0, quad tgeq t_0 $$ which has a retarded argument $r(t)$ and an advanced argument $p(t)$. We obtain oscillation and non-oscillation conditions which are closed to be necessary. We provide exa...

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Bibliographic Details
Main Authors: Leonid Berezansky, Yury Domshlak
Format: Article
Language:English
Published: Texas State University 2002-04-01
Series:Electronic Journal of Differential Equations
Subjects:
mixed differential equations, oscillation, non-oscillation, Sturmian comparison method.
Online Access:http://ejde.math.txstate.edu/Volumes/2002/31/abstr.html
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spelling doaj-4fd0deb413724b03b71344774cea255b2020-11-25T00:16:03ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912002-04-01200231118Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, IILeonid BerezanskyYury DomshlakWe study the oscillation of solutions to the differential equation $$ dot{x}(t) +a_1(t)x[r(t)]+a_2(t)x[p(t)]=0, quad tgeq t_0 $$ which has a retarded argument $r(t)$ and an advanced argument $p(t)$. We obtain oscillation and non-oscillation conditions which are closed to be necessary. We provide examples to show that our results are best possible and compare them with known results. http://ejde.math.txstate.edu/Volumes/2002/31/abstr.htmlmixed differential equations, oscillation, non-oscillation, Sturmian comparison method.
collection DOAJ
language English
format Article
sources DOAJ
author Leonid Berezansky
Yury Domshlak
spellingShingle Leonid Berezansky
Yury Domshlak
Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II
Electronic Journal of Differential Equations
mixed differential equations, oscillation, non-oscillation, Sturmian comparison method.
author_facet Leonid Berezansky
Yury Domshlak
author_sort Leonid Berezansky
title Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II
title_short Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II
title_full Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II
title_fullStr Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II
title_full_unstemmed Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II
title_sort differential equations with several deviating arguments: sturmian comparison method in oscillation theory, ii
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2002-04-01
description We study the oscillation of solutions to the differential equation $$ dot{x}(t) +a_1(t)x[r(t)]+a_2(t)x[p(t)]=0, quad tgeq t_0 $$ which has a retarded argument $r(t)$ and an advanced argument $p(t)$. We obtain oscillation and non-oscillation conditions which are closed to be necessary. We provide examples to show that our results are best possible and compare them with known results.
topic mixed differential equations, oscillation, non-oscillation, Sturmian comparison method.
url http://ejde.math.txstate.edu/Volumes/2002/31/abstr.html
work_keys_str_mv AT leonidberezansky differentialequationswithseveraldeviatingargumentssturmiancomparisonmethodinoscillationtheoryii
AT yurydomshlak differentialequationswithseveraldeviatingargumentssturmiancomparisonmethodinoscillationtheoryii
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