Asymptotic behavior of solutions of third-order neutral differential equations with discrete and distributed delay

By refining the standard Riccati substitution technique, integral averaging technique and comparison principle, we obtain new oscillation and asymptotic behavior for a class of third-order neutral differential equations with discrete and distributed delay. These criteria dealing with some cases have...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 4; pp. 3851 - 3874
Main Authors Sathish Kumar, M., Ganesan, V.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
delay
differential equation
neutral
oscillation
third order
Online AccessGet full text

Cover

Abstract By refining the standard Riccati substitution technique, integral averaging technique and comparison principle, we obtain new oscillation and asymptotic behavior for a class of third-order neutral differential equations with discrete and distributed delay. These criteria dealing with some cases have not been covered by the existing results in the literature. We present many sufficient conditions and related examples in order to illustrate the main results.
AbstractList By refining the standard Riccati substitution technique, integral averaging technique and comparison principle, we obtain new oscillation and asymptotic behavior for a class of third-order neutral differential equations with discrete and distributed delay. These criteria dealing with some cases have not been covered by the existing results in the literature. We present many sufficient conditions and related examples in order to illustrate the main results.
Author Ganesan, V.
Sathish Kumar, M.
Author_xml – sequence: 1
  givenname: M.
  surname: Sathish Kumar
  fullname: Sathish Kumar, M.
– sequence: 2
  givenname: V.
  surname: Ganesan
  fullname: Ganesan, V.
BookMark eNptUctKBDEQDKLg8-YHzAc4mkkyk-Qo4mNB8KLn0JP0uFlmJ2uSVfbvzboKItKH7kp3F6muY7I_hQkJOW_oJddcXC0hzy8ZLdHSPXLEhOR1p5Xa_1UfkrOUFpRS1jDBpDgi8TptlqscsrdVj3N49yFWYahSGNfZhyltQZ776OoQHcZqwnWOMFbODwNGnLIvAN_WsJv-8HleeslGzFjB5LYgR9-vM5YaR9ickoMBxoRn3_mEvNzdPt881I9P97Ob68facqlyLRslgCpQ2uleWUq7lg_SyV474ayUqPuOYxFisVUdgxb6BoS2oi3NkvkJme14XYCFWUW_hLgxAbz5egjx1UAsukc0HTqOVHLWCSWo7jXQYXDMOdu5XlNWuNiOy8aQUsTBWJ-_JJdj-NE01GxNMFsTzLcJZeniz9LPJ_4d_wRD644S
CitedBy_id crossref_primary_10_1088_1742_6596_1850_1_012054
crossref_primary_10_3390_sym15020553
crossref_primary_10_3390_fractalfract5030095
crossref_primary_10_3390_sym13081485
crossref_primary_10_1088_1742_6596_1850_1_012091
crossref_primary_10_3390_fractalfract5040156
crossref_primary_10_3390_sym15122105
crossref_primary_10_1016_j_chaos_2024_115737
crossref_primary_10_3390_math9091021
crossref_primary_10_3390_axioms10030192
Cites_doi 10.1134/S001226611106005X
10.1007/s40840-014-0035-7
10.1016/j.automatica.2018.04.016
10.22436/jnsa.009.12.22
10.1002/mma.3153
10.1016/j.sysconle.2018.05.015
10.1186/1687-2770-2014-1
10.15826/umj.2017.2.013
10.1016/j.automatica.2017.10.004
10.1016/j.jmaa.2014.02.016
10.1016/j.mcm.2010.02.011
10.1007/BF01324723
10.1186/s13662-015-0739-5
10.22436/jmcs.017.02.01
ContentType Journal Article
CorporateAuthor 1 Department of Mathematics, Paavai Engineering College (Autonomous), Namakkal-637 018, Tamil Nadu, India
2 PG and Research Department of Mathematics, Aringar Anna Government Arts College, Namakkal-637 002, Tamil Nadu, India
CorporateAuthor_xml – name: 2 PG and Research Department of Mathematics, Aringar Anna Government Arts College, Namakkal-637 002, Tamil Nadu, India
– name: 1 Department of Mathematics, Paavai Engineering College (Autonomous), Namakkal-637 018, Tamil Nadu, India
DBID AAYXX
CITATION
DOA
DOI 10.3934/math.2020250
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 2473-6988
EndPage 3874
ExternalDocumentID oai_doaj_org_article_6ed3e0732648409b9a0ffd2ddc6db902
10_3934_math_2020250
GroupedDBID AAYXX
ADBBV
ALMA_UNASSIGNED_HOLDINGS
AMVHM
BCNDV
CITATION
EBS
FRJ
GROUPED_DOAJ
IAO
ITC
M~E
OK1
RAN
ID FETCH-LOGICAL-c378t-7184a08a89d9b8c00653f7d7b9d4dc77e9b63e212ce5862a5ab1a49c45c7749c3
IEDL.DBID DOA
ISSN 2473-6988
IngestDate Wed Aug 27 01:27:06 EDT 2025
Thu Apr 24 23:03:17 EDT 2025
Tue Jul 01 03:56:45 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 4
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c378t-7184a08a89d9b8c00653f7d7b9d4dc77e9b63e212ce5862a5ab1a49c45c7749c3
OpenAccessLink https://doaj.org/article/6ed3e0732648409b9a0ffd2ddc6db902
PageCount 24
ParticipantIDs doaj_primary_oai_doaj_org_article_6ed3e0732648409b9a0ffd2ddc6db902
crossref_citationtrail_10_3934_math_2020250
crossref_primary_10_3934_math_2020250
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2020-01-01
PublicationDateYYYYMMDD 2020-01-01
PublicationDate_xml – month: 01
  year: 2020
  text: 2020-01-01
  day: 01
PublicationDecade 2020
PublicationTitle AIMS mathematics
PublicationYear 2020
Publisher AIMS Press
Publisher_xml – name: AIMS Press
References 23
T. Candan (24)
25
26
H. Wang, G. Chen, Y. Jiang (12)
28
29
Y. Jiang, C. Jiang, T. Li (32)
Q. Zhu, H. Wang (19)
Q. Zhu (20)
V. Ganesan, M. Sathish Kumar (30)
Ch. G. Philos (7)
31
11
34
B. Wang, Q. Zhu (3)
13
15
T. Li, B. Baculíková, J. Džurina (27)
18
Y. Qi, J. Yu (33)
B. Baculíková, J. Džurina (2)
4
Q. Zhu (21)
6
A. N. Stanzhitskii, A. P. Krenevich, I. G. Novak (1)
C. Jiang, T. Li (5)
References_xml – ident: 1
  article-title: i>Asymptotic equivalence of linear stochastic itô</i> systems and oscillation of solutions of linear second-order equations</i
  publication-title: Diff. Equat.
  doi: 10.1134/S001226611106005X
– ident: 11
  article-title: i>Oscillation criteria for delay and advanced differential equations with nonmonotone arguments</i
– ident: 23
  article-title: i>Oscillation criteria for even-order nonlinear neutral differential equations of mixed type</i
– ident: 33
  article-title: i>Oscillation of second order nonlinear mixed neutral differential equations with distributed deviating arguments</i
  publication-title: Bull. Malays. Math. Sci. Soc.
  doi: 10.1007/s40840-014-0035-7
– ident: 29
  article-title: i>Oscillation of certain third order nonlinear differential equation with neutral terms</i
– ident: 25
  article-title: i>Comparison theorems for second-order neutral differential equations of mixed type</i
– ident: 3
  article-title: i>Stability analysis of semi-Markov switched stochastic systems</i
  publication-title: Automatica
  doi: 10.1016/j.automatica.2018.04.016
– ident: 5
  article-title: i>Oscillation criteria for third-order nonlinear neutral differential equations with distributed deviating arguments</i
  publication-title: J. Nonlinear Sci. Appl.
  doi: 10.22436/jnsa.009.12.22
– ident: 15
  article-title: i>Asymptotic and oscillatory properties of linear stochastic delay differential equations with vanishing delay</i
– ident: 24
  article-title: i>Oscillation criteria and asymptotic properties of solutions of third-order nonlinear neutral differential equations</i
  publication-title: Math. Method. Appl. Sci.
  doi: 10.1002/mma.3153
– ident: 20
  article-title: i>Stability analysis of stochastic delay differential equations with Lévy noise</i
  publication-title: Syst. Control Lett.
  doi: 10.1016/j.sysconle.2018.05.015
– ident: 27
  article-title: i>Oscillatory behavior of second-order nonlinear neutral differential equations with distributed deviating arguments</i
  publication-title: Bound. Value Probl.
  doi: 10.1186/1687-2770-2014-1
– ident: 6
  article-title: i>Asymptotic behavior of third-order differential equations with nonpositive neutral coefficients and distributed deviating arguments</i
– ident: 30
  article-title: i>On the oscillation of a third order nonlinear differential equations with neutral type</i
  publication-title: Ural Math. J.
  doi: 10.15826/umj.2017.2.013
– ident: 19
  article-title: i>Output feedback stabilization of stochastic feed forward systems with unknown control coefficients and unknown output function</i
  publication-title: Automatica
  doi: 10.1016/j.automatica.2017.10.004
– ident: 21
  article-title: i>Asymptotic stability in the pth moment for stochastic differential equations with Lévy noise</i
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2014.02.016
– ident: 26
  article-title: i>Oscillation results for second-order neutral differential equations of mixed type</i
– ident: 13
  article-title: i>Oscillation in solutions of stochastic delay differential equations with richard's nonlinearity</i
– ident: 2
  article-title: i>Oscillation of third-order neutral differential equations</i
  publication-title: Math. Comput. Model.
  doi: 10.1016/j.mcm.2010.02.011
– ident: 31
  article-title: t al. Nonlinear oscillation of certain third-order neutral differential equation with distributed delay</i
– ident: 4
  article-title: t al. Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments</i
– ident: 7
  article-title: i>Oscillation theorems for linear difierential equations of second order</i
  publication-title: Arch. Math.
  doi: 10.1007/BF01324723
– ident: 18
  article-title: i>Some new oscillatory behavior of certain third-order nonlinear neutral differential equations of mixed type</i
– ident: 34
  article-title: t al. Oscillatory behavior of solutions of certain third-order mixed neutral functional differential equations</i
– ident: 32
  article-title: i>Oscillatory behavior of third-order nonlinear neutral delay differential equations</i
  publication-title: Adv. Differ. Equ.
  doi: 10.1186/s13662-015-0739-5
– ident: 28
  article-title: i>Asymptotic behavior of higher-order quasilinear neutral differential equations</i
– ident: 12
  article-title: t al. Asymptotic behavior of third-order neutral differential equations with distributed deviating arguments</i
  publication-title: J. Math. Comput. Sci.
  doi: 10.22436/jmcs.017.02.01
SSID ssj0002124274
Score 2.1974914
Snippet By refining the standard Riccati substitution technique, integral averaging technique and comparison principle, we obtain new oscillation and asymptotic...
SourceID doaj
crossref
SourceType Open Website
Enrichment Source
Index Database
StartPage 3851
SubjectTerms delay
differential equation
neutral
oscillation
third order
Title Asymptotic behavior of solutions of third-order neutral differential equations with discrete and distributed delay
URI https://doaj.org/article/6ed3e0732648409b9a0ffd2ddc6db902
Volume 5
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8NAEF7Ekx7EJ9YXe9CThKbZ3WxyrGIpgp4s9Bb2iUJNa5oe-u-dyaahHsSLp2SSISyTybwy-w0ht5kfsDSWKhLSJhFPnYuUkDxiluGYJC1S13RbvKbjCX-eiunWqC_sCQvwwEFw_dRZ5kAPsRMLchGdq9h7m1hrUqvzACMJPm8rmUIbDAaZQ74VOt1Zzngf4j_895Cgz__hg7ag-hufMjokB20wSIdhEUdkx5XHZP-lQ1JdnpBquFx_Luo5UHSzpZ7OPe1UBon6_aOyUYOiSUu3wuIF3Uw-gS94Rt1XQPReUqy7UtyKW0G0TFVpkQhTrxycu5lan5LJ6OntcRy1cxIiw2RWR-BeuIozleU215lp4Ga9tFLnllsjpct1yhyIxDgBCYwSSg8Uzw0XcBOO7IzslvPSnRMqYg8hlbWQOCluhFeJTaUHE-iNk34geuR-I7nCtCDiOMtiVkAygXIuUM5FK-ceueu4FwE84xe-B3wJHQ9CXjcXQBGKVhGKvxTh4j8eckn2cE2hxnJFdutq5a4h6qj1TaNg397J2UQ
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Asymptotic+behavior+of+solutions+of+third-order+neutral+differential+equations+with+discrete+and+distributed+delay&rft.jtitle=AIMS+mathematics&rft.au=Sathish+Kumar%2C+M.&rft.au=Ganesan%2C+V.&rft.date=2020-01-01&rft.issn=2473-6988&rft.eissn=2473-6988&rft.volume=5&rft.issue=4&rft.spage=3851&rft.epage=3874&rft_id=info:doi/10.3934%2Fmath.2020250&rft.externalDBID=n%2Fa&rft.externalDocID=10_3934_math_2020250
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2473-6988&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2473-6988&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2473-6988&client=summon