Non-autonomous nonlinear integro-differential equations with infinite delay

In this paper we consider a non-autonomous abstract nonlinear Volterra integro-differential equation with infinite delay in a Banach space. We establish the existence and uniqueness of a strict solution under a certain local Lipschitz condition on the nonlinear map and an integrability condition on...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Nonlinear analysis Jg. 70; H. 7; S. 2642 - 2653
Hauptverfasser:	Bahuguna, D., Pandey, D.N., Ujlayan, A.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier Ltd 01.04.2009 Elsevier
Schlagworte:	Exact sciences and technology Hyperbolic problem Infinite delay Mathematical analysis Mathematics Non-autonomous integro-differential equation Phase space Sciences and techniques of general use Non-autonomous integro-differential equation Infinite delay Phase space Hyperbolic problem Non linear equation Nonlinear analysis Hyperbolic equation Mathematical model Integrodifferential equation Partial differential equation
ISSN:	0362-546X, 1873-5215
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Abstract	In this paper we consider a non-autonomous abstract nonlinear Volterra integro-differential equation with infinite delay in a Banach space. We establish the existence and uniqueness of a strict solution under a certain local Lipschitz condition on the nonlinear map and an integrability condition on the kernel.
AbstractList	In this paper we consider a non-autonomous abstract nonlinear Volterra integro-differential equation with infinite delay in a Banach space. We establish the existence and uniqueness of a strict solution under a certain local Lipschitz condition on the nonlinear map and an integrability condition on the kernel.
Author	Bahuguna, D. Pandey, D.N. Ujlayan, A.
Author_xml	– sequence: 1 givenname: D. surname: Bahuguna fullname: Bahuguna, D. email: dhiren@iitk.ac.in – sequence: 2 givenname: D.N. surname: Pandey fullname: Pandey, D.N. email: dwij@iitk.ac.in – sequence: 3 givenname: A. surname: Ujlayan fullname: Ujlayan, A. email: ujlayan@iitk.ac.in
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21230967$$DView record in Pascal Francis
BookMark	eNp9kDtPwzAUhS0EEuWxM2ZhTLiOE6dlQ4iXQLCAxGbd2NfgKrXBdkH8e1KKGJBgOsv3HemcHbbpgyfGDjhUHLg8mlceqxpgWoGooOUbbMKnnSjbmrebbAJC1mXbyMdttpPSHAB4J-SEXd8GX-IyBx8WYZmKsXVwnjAWzmd6iqE0zlqK5LPDoaDXJWYXfCreXX4eGeu8y1QYGvBjj21ZHBLtf-cuezg_uz-9LG_uLq5OT25KLeoml1b00GMvjZkRiTFMh1BLaISujSbZm85AixK5bWZ9C9PeUt9yPdXaQtOh2GWH694XTBoHG9Frl9RLdAuMH6rmtYCZ7EYO1pyOIaVI9gfhoFanqbnyqFanKRBqPG1U5C9Fu_y1OEd0w3_i8Vqkcfibo6iSduQ1GRdJZ2WC-1v-BCz9ikc
CODEN	NOANDD
CitedBy_id	crossref_primary_10_1016_j_nahs_2013_08_001 crossref_primary_10_1016_j_na_2011_02_010
Cites_doi	10.1016/S0362-546X(99)00447-2 10.1016/S0362-546X(00)00184-X 10.1016/0362-546X(95)00018-Q 10.1007/BF03025772 10.1016/S0893-9659(04)90092-4 10.1016/j.na.2006.04.009 10.1016/j.jmaa.2006.08.030 10.4064/sm-126-3-219-233 10.1016/j.na.2007.02.038 10.1090/S0002-9947-1974-0382808-3 10.1016/0022-0396(80)90093-5
ContentType	Journal Article
Copyright	2008 Elsevier Ltd 2015 INIST-CNRS
Copyright_xml	– notice: 2008 Elsevier Ltd – notice: 2015 INIST-CNRS
DBID	AAYXX CITATION IQODW
DOI	10.1016/j.na.2008.03.051
DatabaseName	CrossRef Pascal-Francis
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Engineering Mathematics
EISSN	1873-5215
EndPage	2653
ExternalDocumentID	21230967 10_1016_j_na_2008_03_051 S0362546X08002630
GroupedDBID	--K --M -~X .~1 0R~ 123 1B1 1RT 1~. 1~5 29N 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABLJU ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACIWK ACNNM ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD ADTZH AEBSH AECPX AEKER AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 GBLVA HMJ HVGLF HZ~ IHE J1W JJJVA KOM M26 M41 MHUIS MO0 MVM N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SES SEW SME SPC SPCBC SST SSW SSZ T5K TN5 WUQ XPP YQT ZMT ~G- 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ADNMO AEIPS AFJKZ AGQPQ AIIUN ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH
ID	FETCH-LOGICAL-c324t-f3b0bab6dd9ee36ddd7a026043c2dce6bd7d05a6a1f49b508bfeb51c8ccf047a3
ISICitedReferencesCount	3
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000264253700017&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0362-546X
IngestDate	Mon Jul 21 09:14:56 EDT 2025 Sat Nov 29 02:57:50 EST 2025 Tue Nov 18 21:59:08 EST 2025 Fri Feb 23 02:23:31 EST 2024
IsPeerReviewed	true
IsScholarly	true
Issue	7
Keywords	Non-autonomous integro-differential equation Infinite delay Phase space Hyperbolic problem Non linear equation Nonlinear analysis Hyperbolic equation Mathematical model Integrodifferential equation Partial differential equation
Language	English
License	https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c324t-f3b0bab6dd9ee36ddd7a026043c2dce6bd7d05a6a1f49b508bfeb51c8ccf047a3
PageCount	12
ParticipantIDs	pascalfrancis_primary_21230967 crossref_primary_10_1016_j_na_2008_03_051 crossref_citationtrail_10_1016_j_na_2008_03_051 elsevier_sciencedirect_doi_10_1016_j_na_2008_03_051
PublicationCentury	2000
PublicationDate	2009-04-01
PublicationDateYYYYMMDD	2009-04-01
PublicationDate_xml	– month: 04 year: 2009 text: 2009-04-01 day: 01
PublicationDecade	2000
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Nonlinear analysis
PublicationYear	2009
Publisher	Elsevier Ltd Elsevier
Publisher_xml	– name: Elsevier Ltd – name: Elsevier
References	Adimy, Bouzahir, Ezzinbi (b1) 2002; 48 Chang (b3) 2007; 331 Nagel, Sinestrary (b12) 2001; 27 Pazy (b13) 1983 Tanabe (b17) 1979 Kappel, Schappacher (b9) 1980; 37 Liang, Xiao, Casteren (b19) 2004; 17 Chang (b5) 2007; 66 Adimy, Bouzahir, Ezzinbi (b2) 2001; 46 Schumacher (b16) 1978; 64 Rhandi (b20) 1997; 126 Hino, Murkami, Naito (b8) 1991; vol. 1473 Liu (b11) 1998; 7 Ezzinbi (b6) 2003; 116 Chang (b4) 2008; 68 Hale, Kato (b7) 1978; 21 Da Prato, Sinestrary (b14) 1992; 45 Kato (b10) 1970; 17 Travis, Webb (b18) 1974; 200 Da Prato, Sinestrary (b15) 1987; 14 Rhandi (10.1016/j.na.2008.03.051_b20) 1997; 126 Tanabe (10.1016/j.na.2008.03.051_b17) 1979 Da Prato (10.1016/j.na.2008.03.051_b14) 1992; 45 Travis (10.1016/j.na.2008.03.051_b18) 1974; 200 Ezzinbi (10.1016/j.na.2008.03.051_b6) 2003; 116 Kato (10.1016/j.na.2008.03.051_b10) 1970; 17 Schumacher (10.1016/j.na.2008.03.051_b16) 1978; 64 Hale (10.1016/j.na.2008.03.051_b7) 1978; 21 Adimy (10.1016/j.na.2008.03.051_b2) 2001; 46 Chang (10.1016/j.na.2008.03.051_b5) 2007; 66 Liang (10.1016/j.na.2008.03.051_b19) 2004; 17 Da Prato (10.1016/j.na.2008.03.051_b15) 1987; 14 Chang (10.1016/j.na.2008.03.051_b3) 2007; 331 Kappel (10.1016/j.na.2008.03.051_b9) 1980; 37 Liu (10.1016/j.na.2008.03.051_b11) 1998; 7 Adimy (10.1016/j.na.2008.03.051_b1) 2002; 48 Nagel (10.1016/j.na.2008.03.051_b12) 2001; 27 Pazy (10.1016/j.na.2008.03.051_b13) 1983 Chang (10.1016/j.na.2008.03.051_b4) 2008; 68 Hino (10.1016/j.na.2008.03.051_b8) 1991; vol. 1473
References_xml	– volume: 126 start-page: 219 year: 1997 end-page: 233 ident: b20 article-title: Extrapolation methods to solve non-autonomous retarded partial differential equation publication-title: Studia Math. – volume: 331 start-page: 137 year: 2007 end-page: 151 ident: b3 article-title: Solutions to non-autonomous integrodifferential equations with infinite delay publication-title: J. Math. Anal. Appl. – volume: 7 start-page: 427 year: 1998 end-page: 439 ident: b11 article-title: Integrodifferential equations with non-autonomous operators publication-title: Dynam. Systems Appl. – year: 1983 ident: b13 article-title: Semigroup of Linear Operators and Application to Partial Differential Equations – volume: vol. 1473 year: 1991 ident: b8 publication-title: Functional Differential Equations with Infinite Delay – volume: 48 start-page: 323 year: 2002 end-page: 348 ident: b1 article-title: Local existence and stability for some partial functional differential equations with infinite delay publication-title: Nonlinear Anal. – year: 1979 ident: b17 article-title: Equations of Evolution – volume: 66 start-page: 2814 year: 2007 end-page: 2832 ident: b5 article-title: Local existence for retarded Volterra integrodifferential equations with Hille-Yosida operators publication-title: Nonlinear Anal. – volume: 17 start-page: 241 year: 1970 end-page: 258 ident: b10 article-title: Linear evolution equations of “hyperbolic type” publication-title: J. Fac. Sci. Univ. Tokyo Math. Sect. I – volume: 14 start-page: 285 year: 1987 end-page: 344 ident: b15 article-title: Differential operators with nondense domain publication-title: Anner. Sc. Norm. Super. Pisa – volume: 27 start-page: 167 year: 2001 end-page: 186 ident: b12 article-title: Nonlinear hyperbolic Volterra integrodifferential equations publication-title: Nonlinear Anal. – volume: 68 start-page: 2943 year: 2008 end-page: 2956 ident: b4 article-title: Local existence for nonlinear Volterra integrodifferential equations with infinite delay publication-title: Nonlinear Anal. – volume: 116 start-page: 1 year: 2003 end-page: 13 ident: b6 article-title: Existence and stability for some partial functional differential equations publication-title: Electron. J. Differential Equations – volume: 45 start-page: 302 year: 1992 end-page: 321 ident: b14 article-title: Nonautonomous evolution operators of hyperbolic type publication-title: Semigroup Fouram – volume: 64 start-page: 313 year: 1978 end-page: 335 ident: b16 article-title: Existence and continuous dependence for differential equations with unbounded delay publication-title: Arch. Ration. Mech. Anal. – volume: 17 start-page: 473 year: 2004 end-page: 477 ident: b19 article-title: A Notes of semilinear abstract functional and integrodifferential equations with infinite delay publication-title: Appl. Math. Lett. – volume: 37 start-page: 141 year: 1980 end-page: 183 ident: b9 article-title: Some considerations to the fundamental theory of infinite delay equations publication-title: J. Differential Equations – volume: 21 start-page: 11 year: 1978 end-page: 41 ident: b7 article-title: Phase space for retarded equations with infinite delay publication-title: Funkcial. Evac. – volume: 46 start-page: 91 year: 2001 end-page: 112 ident: b2 article-title: Existence for a class of partial differential equations with infinite delay publication-title: Nonlinear Anal. – volume: 200 start-page: 395 year: 1974 end-page: 418 ident: b18 article-title: Existence and stability for partial functional differential equations publication-title: Trans. Amer. Math. Soc. – volume: 17 start-page: 241 year: 1970 ident: 10.1016/j.na.2008.03.051_b10 article-title: Linear evolution equations of “hyperbolic type” publication-title: J. Fac. Sci. Univ. Tokyo Math. Sect. I – volume: 7 start-page: 427 year: 1998 ident: 10.1016/j.na.2008.03.051_b11 article-title: Integrodifferential equations with non-autonomous operators publication-title: Dynam. Systems Appl. – volume: 21 start-page: 11 year: 1978 ident: 10.1016/j.na.2008.03.051_b7 article-title: Phase space for retarded equations with infinite delay publication-title: Funkcial. Evac. – volume: 14 start-page: 285 year: 1987 ident: 10.1016/j.na.2008.03.051_b15 article-title: Differential operators with nondense domain publication-title: Anner. Sc. Norm. Super. Pisa – year: 1983 ident: 10.1016/j.na.2008.03.051_b13 – year: 1979 ident: 10.1016/j.na.2008.03.051_b17 – volume: 46 start-page: 91 year: 2001 ident: 10.1016/j.na.2008.03.051_b2 article-title: Existence for a class of partial differential equations with infinite delay publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(99)00447-2 – volume: 116 start-page: 1 year: 2003 ident: 10.1016/j.na.2008.03.051_b6 article-title: Existence and stability for some partial functional differential equations publication-title: Electron. J. Differential Equations – volume: 48 start-page: 323 year: 2002 ident: 10.1016/j.na.2008.03.051_b1 article-title: Local existence and stability for some partial functional differential equations with infinite delay publication-title: Nonlinear Anal. doi: 10.1016/S0362-546X(00)00184-X – volume: 27 start-page: 167 year: 2001 ident: 10.1016/j.na.2008.03.051_b12 article-title: Nonlinear hyperbolic Volterra integrodifferential equations publication-title: Nonlinear Anal. doi: 10.1016/0362-546X(95)00018-Q – volume: 45 start-page: 302 year: 1992 ident: 10.1016/j.na.2008.03.051_b14 article-title: Nonautonomous evolution operators of hyperbolic type publication-title: Semigroup Fouram doi: 10.1007/BF03025772 – volume: 17 start-page: 473 year: 2004 ident: 10.1016/j.na.2008.03.051_b19 article-title: A Notes of semilinear abstract functional and integrodifferential equations with infinite delay publication-title: Appl. Math. Lett. doi: 10.1016/S0893-9659(04)90092-4 – volume: 66 start-page: 2814 year: 2007 ident: 10.1016/j.na.2008.03.051_b5 article-title: Local existence for retarded Volterra integrodifferential equations with Hille-Yosida operators publication-title: Nonlinear Anal. doi: 10.1016/j.na.2006.04.009 – volume: 331 start-page: 137 year: 2007 ident: 10.1016/j.na.2008.03.051_b3 article-title: Solutions to non-autonomous integrodifferential equations with infinite delay publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2006.08.030 – volume: vol. 1473 year: 1991 ident: 10.1016/j.na.2008.03.051_b8 – volume: 126 start-page: 219 year: 1997 ident: 10.1016/j.na.2008.03.051_b20 article-title: Extrapolation methods to solve non-autonomous retarded partial differential equation publication-title: Studia Math. doi: 10.4064/sm-126-3-219-233 – volume: 68 start-page: 2943 year: 2008 ident: 10.1016/j.na.2008.03.051_b4 article-title: Local existence for nonlinear Volterra integrodifferential equations with infinite delay publication-title: Nonlinear Anal. doi: 10.1016/j.na.2007.02.038 – volume: 64 start-page: 313 year: 1978 ident: 10.1016/j.na.2008.03.051_b16 article-title: Existence and continuous dependence for differential equations with unbounded delay publication-title: Arch. Ration. Mech. Anal. – volume: 200 start-page: 395 year: 1974 ident: 10.1016/j.na.2008.03.051_b18 article-title: Existence and stability for partial functional differential equations publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1974-0382808-3 – volume: 37 start-page: 141 year: 1980 ident: 10.1016/j.na.2008.03.051_b9 article-title: Some considerations to the fundamental theory of infinite delay equations publication-title: J. Differential Equations doi: 10.1016/0022-0396(80)90093-5
SSID	ssj0001736
Score	1.8826587
Snippet	In this paper we consider a non-autonomous abstract nonlinear Volterra integro-differential equation with infinite delay in a Banach space. We establish the...
SourceID	pascalfrancis crossref elsevier
SourceType	Index Database Enrichment Source Publisher
StartPage	2642
SubjectTerms	Exact sciences and technology Hyperbolic problem Infinite delay Mathematical analysis Mathematics Non-autonomous integro-differential equation Phase space Sciences and techniques of general use
Title	Non-autonomous nonlinear integro-differential equations with infinite delay
URI	https://dx.doi.org/10.1016/j.na.2008.03.051
Volume	70
WOSCitedRecordID	wos000264253700017&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-5215 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001736 issn: 0362-546X databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELZgywGEeBQQ5VH5wAWhhGycxPFxRYt4Rki0aG-R7djQFUqXJkH9-Ywf8W4EVIDEJbtrrR0rM7G_Gc98g9ATIvic5UpGOdM8yrQWEVNNaYLGCclyrktbJeLTO1pV5XLJPvhY1c6WE6BtW56fs_V_FTW0gbBN6uxfiDsMCg3wHYQOVxA7XP9I8NVpG_GhN8kKln3VcWGYWFPLDHEajTVReuMsV98GHwxnPbIwgRODQp8Z8sjJiW8VxuGex2TjBP0yfB5cbtlBvDmTahvnDj-Iq9B6vIJhnc91EU88DmwrUMW6wcZUmE3c0Zh-lWe2LCFsLG41LSkBS9fla47LrasT4tWKbq-dhePZ8vtwWjgW4Z_WeOduWMUt96GwJE48ae2UOfujmZOZkkXFBUkuo52U5qycoZ3F68Plm7BlzykpRp4x08GfZ7tAwOl9fodfrq95B2-VduVQtjDK0S10wxsXeOGU4ja6pNpddNMbGtgv490uurbFQgm_3gfq3u4OejvVHxz0B_9Kf3DQH2z0B4_6g63-3EXHLw-PXryKfMWNSAKw7iNNRCK4KJqGKUXgo6HckM5lRKaNVIVoaJPkvOBznTEB2F5oJfK5LKXUSUY5uYdmMC11H-G04TnVeSoyyTKdSAbQUwgAgyAHsBKSPfR8fI619HT0pirK13qMO1zVLfdVUkkNT34PPQ091o6K5YL_klE0tYeSDiLWoEUX9NqfSDHcxuA7sPXpg38a9iG6unmNHqFZfzaox-iK_N6fdGf7Xhd_AO_aouk
linkProvider	Elsevier
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=Non-autonomous+nonlinear+integro-differential+equations+with+infinite+delay&rft.jtitle=Nonlinear+analysis&rft.au=Bahuguna%2C+D.&rft.au=Pandey%2C+D.N.&rft.au=Ujlayan%2C+A.&rft.date=2009-04-01&rft.pub=Elsevier+Ltd&rft.issn=0362-546X&rft.eissn=1873-5215&rft.volume=70&rft.issue=7&rft.spage=2642&rft.epage=2653&rft_id=info:doi/10.1016%2Fj.na.2008.03.051&rft.externalDocID=S0362546X08002630
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0362-546X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0362-546X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0362-546X&client=summon