Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation

Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation

The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation rlu′lγ′+qlxβσl=0, where l≥l0 and ul≔xl+pxϱl. By optimizing the commonly used relationship x>1−pu, we obtain new criteria that give sharper...

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Main Authors: Osama Moaaz, Ali Muhib, Saud Owyed, Emad E. Mahmoud, Aml Abdelnaser
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/6665103
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spelling doaj-31b00ec633ed43a283aa1523abf166ec2021-03-29T00:09:31ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/6665103Second-Order Neutral Differential Equations: Improved Criteria for Testing the OscillationOsama Moaaz0Ali Muhib1Saud Owyed2Emad E. Mahmoud3Aml Abdelnaser4Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Mathematics and StatisticsDepartment of MathematicsThe main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation rlu′lγ′+qlxβσl=0, where l≥l0 and ul≔xl+pxϱl. By optimizing the commonly used relationship x>1−pu, we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.http://dx.doi.org/10.1155/2021/6665103
collection DOAJ
language English
format Article
sources DOAJ
author Osama Moaaz
Ali Muhib
Saud Owyed
Emad E. Mahmoud
Aml Abdelnaser
spellingShingle Osama Moaaz
Ali Muhib
Saud Owyed
Emad E. Mahmoud
Aml Abdelnaser
Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation
Journal of Mathematics
author_facet Osama Moaaz
Ali Muhib
Saud Owyed
Emad E. Mahmoud
Aml Abdelnaser
author_sort Osama Moaaz
title Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation
title_short Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation
title_full Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation
title_fullStr Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation
title_full_unstemmed Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation
title_sort second-order neutral differential equations: improved criteria for testing the oscillation
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation rlu′lγ′+qlxβσl=0, where l≥l0 and ul≔xl+pxϱl. By optimizing the commonly used relationship x>1−pu, we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.
url http://dx.doi.org/10.1155/2021/6665103
work_keys_str_mv AT osamamoaaz secondorderneutraldifferentialequationsimprovedcriteriafortestingtheoscillation
AT alimuhib secondorderneutraldifferentialequationsimprovedcriteriafortestingtheoscillation
AT saudowyed secondorderneutraldifferentialequationsimprovedcriteriafortestingtheoscillation
AT emademahmoud secondorderneutraldifferentialequationsimprovedcriteriafortestingtheoscillation
AT amlabdelnaser secondorderneutraldifferentialequationsimprovedcriteriafortestingtheoscillation
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