Normalized homoclinic solutions of discrete nonlocal double phase problems

The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if...

Full description

Saved in:
Bibliographic Details
Published inBulletin of mathematical sciences Vol. 14; no. 2
Main Authors Xiang, Mingqi, Ma, Yunfeng, Yang, Miaomiao
Format Journal Article
LanguageEnglish
Published World Scientific Publishing 01.08.2024
Subjects
discrete fractional -Laplacian
Double phase problem
homoclinic solutions
normalized solutions
Online AccessGet full text

Cover

Abstract The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula: see text], and [Formula: see text]([Formula: see text] or [Formula: see text], [Formula: see text] or [Formula: see text]) is the discrete fractional [Formula: see text]-Laplacian. By variational methods, we discuss the existence of non-negative normalized homoclinic solutions under the conditions that the nonlinear term satisfies sublinear growth or superlinear growth conditions. In particular, we establish the compactness of the associated energy functional of the problem without weights. Our paper is the first time to deal with the existence of normalized solutions for discrete double phase problems.
AbstractList The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula: see text], and [Formula: see text]([Formula: see text] or [Formula: see text], [Formula: see text] or [Formula: see text]) is the discrete fractional [Formula: see text]-Laplacian. By variational methods, we discuss the existence of non-negative normalized homoclinic solutions under the conditions that the nonlinear term satisfies sublinear growth or superlinear growth conditions. In particular, we establish the compactness of the associated energy functional of the problem without weights. Our paper is the first time to deal with the existence of normalized solutions for discrete double phase problems.
The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: ( − Δ𝔻)pαu(k) + μ(−Δ 𝔻)qβu(k) + ω(k)|u(k)|p−2u(k) = λ|u(k)|q−2u(k) + h(k)|u(k)|r−2u(k) for k ∈ ℤ,∑k∈ℤ|u(k)|q = ρq > 0, u(k) → 0 as |k|→∞, where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula: see text], and [Formula: see text]([Formula: see text] or [Formula: see text], [Formula: see text] or [Formula: see text]) is the discrete fractional [Formula: see text]-Laplacian. By variational methods, we discuss the existence of non-negative normalized homoclinic solutions under the conditions that the nonlinear term satisfies sublinear growth or superlinear growth conditions. In particular, we establish the compactness of the associated energy functional of the problem without weights. Our paper is the first time to deal with the existence of normalized solutions for discrete double phase problems.
Author Yang, Miaomiao
Ma, Yunfeng
Xiang, Mingqi
Author_xml – sequence: 1
  givenname: Mingqi
  orcidid: 0000-0002-0712-7149
  surname: Xiang
  fullname: Xiang, Mingqi
  organization: College of Science, Civil Aviation, University of China, Tianjin 300300, P. R. China
– sequence: 2
  givenname: Yunfeng
  surname: Ma
  fullname: Ma, Yunfeng
  organization: College of Science, Civil Aviation, University of China, Tianjin 300300, P. R. China
– sequence: 3
  givenname: Miaomiao
  surname: Yang
  fullname: Yang, Miaomiao
  organization: School of Mathematics and Statistics, Qilu University of Technology (Shandong, Academy of Sciences), Jinan 250353, P. R. China
BookMark eNplkMtOwzAQRS1UJErpB7DLDxT8ih0vUcWjqIIFsI4ce0xdOXFlpwv4elyKumEzj6vRuaN7iSZDHACha4JvCOH09o0IwZnAkvIaY8zEGZoepAUTpJ6cZiwv0DznbTnBtVRKqil6fomp18F_g602sY8m-MGbKsewH30cchVdZX02CUaoim2IRofKxn0XoNptdC41xbL0-QqdOx0yzP_6DH083L8vnxbr18fV8m69MAyLsfwhqasZx9QoaUA4bpQTnbJAG4Edtg6cNoZKJhpLCZOgCahGUKw73VjBZmh15Nqot-0u-V6nrzZq3_4KMX22Oo3eBGgZ5cXTUKAgOa2dAqIY6yiz1GlFZGGRI8ukmHMCd-IR3B6ybf9ly34AibRt3Q
Cites_doi 10.1016/S0375-9601(00)00201-2
10.1515/fca-2016-0018
10.1007/s10231-018-0796-y
10.1080/03605300600987306
10.1515/anona-2020-0018
10.1007/s12220-023-01497-2
10.1016/j.jfa.2020.108610
10.1007/s00033-022-01741-9
10.1007/s00526-020-01814-5
10.1016/j.na.2013.08.011
10.1007/978-3-642-25361-4_3
10.1515/anona-2022-0252
10.1016/j.jmaa.2009.02.038
10.1016/j.na.2003.11.012
10.1515/anona-2022-0300
10.1007/s12220-022-01171-z
10.1006/jdeq.1997.3247
10.1007/978-1-4612-4146-1
10.1515/anona-2020-0194
10.1016/j.bulsci.2011.12.004
10.1016/j.aim.2018.03.023
10.1088/1361-6544/aaf2e0
10.1007/s12220-023-01463-y
10.1016/j.jmaa.2011.12.032
10.1016/j.na.2020.111886
10.1007/978-1-4419-7515-7
10.1515/anona-2020-0193
10.1007/s00245-016-9330-z
10.1016/j.jmaa.2013.02.011
10.1007/s10473-022-0323-5
10.1515/anona-2022-0291
10.1016/j.matpur.2020.08.011
10.1142/S0219199719500652
10.1016/j.jde.2013.06.016
10.1016/j.amc.2022.127443
10.1016/S0362-546X(96)00021-1
10.3934/dcds.2020379
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.1142/S1664360724500036
DatabaseName CrossRef
Open Access: DOAJ - Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
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 1664-3615
ExternalDocumentID oai_doaj_org_article_324306c2e2e7425f9e1933b23d2fa917
10_1142_S1664360724500036
GroupedDBID -A0
2VQ
4.4
40G
5VS
8FE
8FG
AAKKN
AAYXX
AAYZJ
ABEEZ
ABJCF
ACACY
ACGFS
ACIPV
ACIWK
ACULB
ADBBV
ADINQ
AENEX
AFGXO
AFKRA
AHBXF
AHBYD
AHSBF
AHYZX
ALMA_UNASSIGNED_HOLDINGS
AMKLP
BCNDV
BENPR
BGLVJ
C24
C6C
CCPQU
CITATION
EBS
EJD
GROUPED_DOAJ
H4N
HCIFZ
HZ~
IAO
ISR
ITC
J9A
KQ8
L6V
M7S
M~E
O9-
OK1
PIMPY
PROAC
PTHSS
RSV
RWJ
SMT
SOJ
U2A
ID FETCH-LOGICAL-c306t-3672f53402c97ce6f4c9f6b9de2860f0dfefacc27368d2137ea1e98620aba8d63
IEDL.DBID DOA
ISSN 1664-3607
IngestDate Tue Oct 22 15:06:01 EDT 2024
Thu Sep 26 20:36:26 EDT 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c306t-3672f53402c97ce6f4c9f6b9de2860f0dfefacc27368d2137ea1e98620aba8d63
ORCID 0000-0002-0712-7149
OpenAccessLink https://doaj.org/article/324306c2e2e7425f9e1933b23d2fa917
ParticipantIDs doaj_primary_oai_doaj_org_article_324306c2e2e7425f9e1933b23d2fa917
crossref_primary_10_1142_S1664360724500036
PublicationCentury 2000
PublicationDate 2024-08-01
PublicationDateYYYYMMDD 2024-08-01
PublicationDate_xml – month: 08
  year: 2024
  text: 2024-08-01
  day: 01
PublicationDecade 2020
PublicationTitle Bulletin of mathematical sciences
PublicationYear 2024
Publisher World Scientific Publishing
Publisher_xml – name: World Scientific Publishing
References S1664360724500036BIB031
S1664360724500036BIB030
S1664360724500036BIB013
S1664360724500036BIB035
S1664360724500036BIB012
Dimitrov N. (S1664360724500036BIB015) 2020; 25
S1664360724500036BIB010
S1664360724500036BIB032
Molica Bisci G. (S1664360724500036BIB034) 2015
S1664360724500036BIB017
S1664360724500036BIB039
S1664360724500036BIB016
S1664360724500036BIB038
S1664360724500036BIB037
Berestycki H. (S1664360724500036BIB006) 1983; 82
Diblik J. (S1664360724500036BIB014) 2023; 12
Ju X. (S1664360724500036BIB025) 2020; 559
S1664360724500036BIB036
S1664360724500036BIB019
Cheng J. (S1664360724500036BIB011) 2023; 12
S1664360724500036BIB018
Mihăilescu M. (S1664360724500036BIB033) 2011; 38
Applebaum D. (S1664360724500036BIB004) 2004; 51
S1664360724500036BIB042
S1664360724500036BIB041
Valdinoci E. (S1664360724500036BIB040) 2009; 49
S1664360724500036BIB002
S1664360724500036BIB024
S1664360724500036BIB046
S1664360724500036BIB001
S1664360724500036BIB023
S1664360724500036BIB045
S1664360724500036BIB022
S1664360724500036BIB044
S1664360724500036BIB021
S1664360724500036BIB043
S1664360724500036BIB028
S1664360724500036BIB005
S1664360724500036BIB027
S1664360724500036BIB026
S1664360724500036BIB003
S1664360724500036BIB047
S1664360724500036BIB009
Iannizzotto A. (S1664360724500036BIB020) 2014; 27
S1664360724500036BIB008
S1664360724500036BIB007
S1664360724500036BIB029
References_xml – ident: S1664360724500036BIB026
  doi: 10.1016/S0375-9601(00)00201-2
– ident: S1664360724500036BIB013
  doi: 10.1515/fca-2016-0018
– volume: 82
  start-page: 247
  year: 1983
  ident: S1664360724500036BIB006
  publication-title: Arch. Ration. Mech. Anal.
  contributor:
    fullname: Berestycki H.
– volume: 12
  start-page: 20230105-1
  issue: 1
  year: 2023
  ident: S1664360724500036BIB014
  publication-title: Adv. Nonlinear Anal.
  contributor:
    fullname: Diblik J.
– ident: S1664360724500036BIB007
  doi: 10.1007/s10231-018-0796-y
– ident: S1664360724500036BIB010
  doi: 10.1080/03605300600987306
– ident: S1664360724500036BIB022
  doi: 10.1515/anona-2020-0018
– ident: S1664360724500036BIB043
  doi: 10.1007/s12220-023-01497-2
– ident: S1664360724500036BIB039
  doi: 10.1016/j.jfa.2020.108610
– ident: S1664360724500036BIB002
  doi: 10.1007/s00033-022-01741-9
– ident: S1664360724500036BIB030
  doi: 10.1007/s00526-020-01814-5
– ident: S1664360724500036BIB018
  doi: 10.1016/j.na.2013.08.011
– volume: 25
  start-page: 555
  year: 2020
  ident: S1664360724500036BIB015
  publication-title: Discrete Contin. Dyn. Syst. Ser. B
  contributor:
    fullname: Dimitrov N.
– ident: S1664360724500036BIB009
  doi: 10.1007/978-3-642-25361-4_3
– ident: S1664360724500036BIB029
  doi: 10.1515/anona-2022-0252
– ident: S1664360724500036BIB008
  doi: 10.1016/j.jmaa.2009.02.038
– ident: S1664360724500036BIB001
  doi: 10.1016/j.na.2003.11.012
– ident: S1664360724500036BIB027
  doi: 10.1515/anona-2022-0300
– ident: S1664360724500036BIB028
  doi: 10.1007/s12220-022-01171-z
– ident: S1664360724500036BIB032
  doi: 10.1006/jdeq.1997.3247
– ident: S1664360724500036BIB042
  doi: 10.1007/978-1-4612-4146-1
– ident: S1664360724500036BIB046
  doi: 10.1515/anona-2020-0194
– ident: S1664360724500036BIB016
  doi: 10.1016/j.bulsci.2011.12.004
– ident: S1664360724500036BIB012
  doi: 10.1016/j.aim.2018.03.023
– ident: S1664360724500036BIB035
  doi: 10.1088/1361-6544/aaf2e0
– ident: S1664360724500036BIB037
  doi: 10.1007/s12220-023-01463-y
– ident: S1664360724500036BIB038
  doi: 10.1016/j.jmaa.2011.12.032
– volume: 49
  start-page: 33
  year: 2009
  ident: S1664360724500036BIB040
  publication-title: Bol. Soc. Esp. Mat. Apl. Se MA
  contributor:
    fullname: Valdinoci E.
– ident: S1664360724500036BIB045
  doi: 10.1016/j.na.2020.111886
– ident: S1664360724500036BIB017
  doi: 10.1007/978-1-4419-7515-7
– ident: S1664360724500036BIB031
  doi: 10.1515/anona-2020-0193
– ident: S1664360724500036BIB036
  doi: 10.1007/s00245-016-9330-z
– volume-title: Variational Methods for Nonlocal Fractional Problems
  year: 2015
  ident: S1664360724500036BIB034
  contributor:
    fullname: Molica Bisci G.
– ident: S1664360724500036BIB021
  doi: 10.1016/j.jmaa.2013.02.011
– volume: 51
  start-page: 1336
  year: 2004
  ident: S1664360724500036BIB004
  publication-title: Notices Amer. Math. Soc.
  contributor:
    fullname: Applebaum D.
– ident: S1664360724500036BIB044
  doi: 10.1007/s10473-022-0323-5
– ident: S1664360724500036BIB041
  doi: 10.1515/anona-2022-0291
– volume: 559
  start-page: 2020
  year: 2020
  ident: S1664360724500036BIB025
  publication-title: Adv. Difference Equations
  contributor:
    fullname: Ju X.
– volume: 38
  start-page: 277
  year: 2011
  ident: S1664360724500036BIB033
  publication-title: Topol. Methods Nonlinear Anal.
  contributor:
    fullname: Mihăilescu M.
– ident: S1664360724500036BIB003
  doi: 10.1016/j.matpur.2020.08.011
– volume: 12
  start-page: 20220272-1
  issue: 1
  year: 2023
  ident: S1664360724500036BIB011
  publication-title: Adv. Nonlinear Anal.
  contributor:
    fullname: Cheng J.
– ident: S1664360724500036BIB019
  doi: 10.1142/S0219199719500652
– ident: S1664360724500036BIB005
  doi: 10.1016/j.jde.2013.06.016
– ident: S1664360724500036BIB024
  doi: 10.1016/j.amc.2022.127443
– volume: 27
  start-page: 35
  year: 2014
  ident: S1664360724500036BIB020
  publication-title: Differ. Integral Equ.
  contributor:
    fullname: Iannizzotto A.
– ident: S1664360724500036BIB023
  doi: 10.1016/S0362-546X(96)00021-1
– ident: S1664360724500036BIB047
  doi: 10.3934/dcds.2020379
SSID ssj0000579979
ssib050729703
ssib041538293
Score 2.3485968
Snippet The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional...
SourceID doaj
crossref
SourceType Open Website
Aggregation Database
SubjectTerms discrete fractional -Laplacian
Double phase problem
homoclinic solutions
normalized solutions
Title Normalized homoclinic solutions of discrete nonlocal double phase problems
URI https://doaj.org/article/324306c2e2e7425f9e1933b23d2fa917
Volume 14
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8NAEF6kJz2IT6wv9uBJCE02-zyqWEqlBdFCb2E3maVCNaWPi7_e2SSWiAcvXnIYNq9vJplv2J1vCblhIGTqvIwgVyzioG1kuYmjQgmWGx_nedUoPBrLwYQPp2La2uorrAmr5YFr4HqY8JHV4hkMsIoT3gBSjtSxtGDeYq1R_X1j0yqmMJJ4-I5biUwEfWzVzDfWqt_KmEqIL5GSR6mMVTPlmXDWewnGYGNcVIotP5JWS9u_SkL9A7LfsEd6Vz_1IdmBjyOyN9pKr66OyXAcWOj87RMKOivfy7r1kW5DjJaehlbcJbJlirV_lcxoUW7cHOhihkmNNpvMrE7IpP_4-jCImg0TohwxWuNrKOZFiiVhblQO0nOEWzpTANMy9nHhwVtEX6VSFyxJFdgEDNY0sXVWFzI9JR28MZwRKqVyCXMCEH2uAVycA47SVjGrjdBdcvuNSLaodTGyuseZZb_g65L7gNl2YJC0rgzo6KxxdPaXo8__4yIXZJchK6lX8F2Sznq5gStkFWt3XQUQHp-e9RcptcOc
link.rule.ids 315,783,787,867,2109,27938,27939
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=Normalized+homoclinic+solutions+of+discrete+nonlocal+double+phase+problems&rft.jtitle=Bulletin+of+mathematical+sciences&rft.au=Mingqi+Xiang&rft.au=Yunfeng+Ma&rft.au=Miaomiao+Yang&rft.date=2024-08-01&rft.pub=World+Scientific+Publishing&rft.issn=1664-3607&rft.eissn=1664-3615&rft.volume=14&rft.issue=2&rft_id=info:doi/10.1142%2FS1664360724500036&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_324306c2e2e7425f9e1933b23d2fa917
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1664-3607&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1664-3607&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1664-3607&client=summon