Normalized solutions for the p-Laplacian equation with a trapping potential

In this article, we are concerned with normalized solutions for the -Laplacian equation with a trapping potential and -supercritical growth, where or The solutions correspond to critical points of the underlying energy functional subject to the -norm constraint, namely, for given When we show that s...

Full description

Saved in:
Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 12; no. 1; pp. 457 - 472
Main Authors Wang, Chao, Sun, Juntao
Format Journal Article
LanguageEnglish
Published De Gruyter 27.03.2023
Subjects
35J20
35J60
35J92
Laplacian equation
normalized solutions
p-laplacian equation
variational methods
Online AccessGet full text

Cover

Abstract In this article, we are concerned with normalized solutions for the -Laplacian equation with a trapping potential and -supercritical growth, where or The solutions correspond to critical points of the underlying energy functional subject to the -norm constraint, namely, for given When we show that such problem has a ground state with positive energy for small enough. When we show that such problem has at least two solutions both with positive energy, which one is a ground state and the other one is a high-energy solution.
AbstractList In this article, we are concerned with normalized solutions for the -Laplacian equation with a trapping potential and -supercritical growth, where or The solutions correspond to critical points of the underlying energy functional subject to the -norm constraint, namely, for given When we show that such problem has a ground state with positive energy for small enough. When we show that such problem has at least two solutions both with positive energy, which one is a ground state and the other one is a high-energy solution.
In this article, we are concerned with normalized solutions for the p p -Laplacian equation with a trapping potential and L r {L}^{r} -supercritical growth, where r = p r=p or 2 . 2. The solutions correspond to critical points of the underlying energy functional subject to the L r {L}^{r} -norm constraint, namely, ∫ R N ∣ u ∣ r d x = c {\int }_{{{\mathbb{R}}}^{N}}| u{| }^{r}{\rm{d}}x=c for given c > 0 . c\gt 0. When r = p , r=p, we show that such problem has a ground state with positive energy for c c small enough. When r = 2 , r=2, we show that such problem has at least two solutions both with positive energy, which one is a ground state and the other one is a high-energy solution.
In this article, we are concerned with normalized solutions for the pp -Laplacian equation with a trapping potential and Lr{L}^{r}-supercritical growth, where r=pr=p or 2.2. The solutions correspond to critical points of the underlying energy functional subject to the Lr{L}^{r}-norm constraint, namely, ∫RN∣u∣rdx=c{\int }_{{{\mathbb{R}}}^{N}}| u{| }^{r}{\rm{d}}x=c for given c>0.c\gt 0. When r=p,r=p, we show that such problem has a ground state with positive energy for cc small enough. When r=2,r=2, we show that such problem has at least two solutions both with positive energy, which one is a ground state and the other one is a high-energy solution.
Author Wang, Chao
Sun, Juntao
Author_xml – sequence: 1
  givenname: Chao
  surname: Wang
  fullname: Wang, Chao
  email: sxwc1310@163.com
  organization: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, PR China
– sequence: 2
  givenname: Juntao
  surname: Sun
  fullname: Sun, Juntao
  email: jtsun@sdut.edu.cn
  organization: School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, PR China
BookMark eNp1kE1LxDAQhoMo-Hn2mj9QzSRNm3gT8QsXvSh4C9M0WbPUpqZZRH-93V0FEcxlJhOel8yzT7b72DtCjoGdgAR5itMdC844LxjXsEX2OGgotGTP27_6XXI0jgs2HSWhrtkeubuP6RW78OlaOsZumUPsR-pjovnF0aGY4dChDdhT97bE1St9D_mFIs0JhyH0czrE7PocsDskOx670R191wPydHX5eHFTzB6uby_OZ4UVWudCKsGbsq6U415B02gm6so3XIAtEQSiq3wp0AtleaugqoWspLAemfAta6w4ILeb3DbiwgwpvGL6MBGDWQ9imhtMOdjOGVAe60qCZshLVFajVFo22EgBwFU5ZclNlk1xHJPzxoa83nPaL3QGmFkJNmvBZiXYrARP3Okf7ucf_xNnG-Idu-xS6-Zp-TE1ZhGXqZ98_UcCB_EF8eKUSg
CitedBy_id crossref_primary_10_1515_forum_2023_0366
crossref_primary_10_1515_anona_2024_0024
crossref_primary_10_1007_s00033_024_02408_3
crossref_primary_10_1515_anona_2024_0042
crossref_primary_10_1007_s13324_025_01011_7
crossref_primary_10_1515_anona_2024_0007
crossref_primary_10_1515_anona_2024_0038
crossref_primary_10_1088_1361_6544_adbc3b
crossref_primary_10_1515_anona_2024_0004
crossref_primary_10_3390_fractalfract8060310
crossref_primary_10_1007_s12220_023_01504_6
crossref_primary_10_1007_s12220_023_01497_2
crossref_primary_10_1142_S1664360724500036
Cites_doi 10.1016/j.jde.2020.05.016
10.1137/21M1463136
10.1007/s00220-017-2866-1
10.1080/03605308908820654
10.1016/j.anihpc.2008.06.001
10.1016/S0362-546X(96)00021-1
10.1016/j.na.2016.10.002
10.1512/iumj.2000.49.1893
10.1007/PL00001512
10.1137/15M1015959
10.1016/j.jfa.2017.01.025
10.1007/s002050050163
10.1137/050624522
10.1063/1.1703944
10.1080/03605309308820960
10.1007/s00030-008-7021-4
10.1016/j.na.2005.09.035
10.1007/BF00251502
10.1007/s43034-020-00101-w
10.1016/j.anihpc.2015.01.005
10.1007/s11005-013-0667-9
10.1137/19M1243907
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.1515/anona-2022-0291
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList
CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: Acceso a contenido Full Text - Doaj
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2191-950X
EndPage 472
ExternalDocumentID oai_doaj_org_article_18fa765190a24a8c9a5895bab5311284
10_1515_anona_2022_0291
10_1515_anona_2022_0291121
GroupedDBID 0R~
0~D
4.4
AAFPC
AAFWJ
AAQCX
AASOL
AASQH
ABAOT
ABAQN
ABFKT
ABIQR
ABSOE
ABUVI
ABXMZ
ACGFS
ACXLN
ACZBO
ADGQD
ADGYE
ADJVZ
ADOZN
AEJTT
AENEX
AEQDQ
AEXIE
AFBAA
AFBDD
AFCXV
AFPKN
AFQUK
AHGSO
AIERV
AJATJ
AKXKS
ALMA_UNASSIGNED_HOLDINGS
AMVHM
BAKPI
BBCWN
CFGNV
EBS
GROUPED_DOAJ
HZ~
IY9
J9A
O9-
OK1
QD8
SA.
AAYXX
CITATION
ID FETCH-LOGICAL-c399t-5832b4768e2f81bb90376fb231c4a13aae6f43af38c2d816735653cfa03fd0bc3
IEDL.DBID DOA
ISSN 2191-950X
IngestDate Wed Aug 27 01:25:56 EDT 2025
Thu Apr 24 23:12:29 EDT 2025
Tue Jul 01 00:37:49 EDT 2025
Thu Jul 10 10:33:04 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
License This work is licensed under the Creative Commons Attribution 4.0 International License.
http://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c399t-5832b4768e2f81bb90376fb231c4a13aae6f43af38c2d816735653cfa03fd0bc3
OpenAccessLink https://doaj.org/article/18fa765190a24a8c9a5895bab5311284
PageCount 14
ParticipantIDs doaj_primary_oai_doaj_org_article_18fa765190a24a8c9a5895bab5311284
crossref_citationtrail_10_1515_anona_2022_0291
crossref_primary_10_1515_anona_2022_0291
walterdegruyter_journals_10_1515_anona_2022_0291121
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2023-03-27
PublicationDateYYYYMMDD 2023-03-27
PublicationDate_xml – month: 03
  year: 2023
  text: 2023-03-27
  day: 27
PublicationDecade 2020
PublicationTitle Advances in nonlinear analysis
PublicationYear 2023
Publisher De Gruyter
Publisher_xml – name: De Gruyter
References 2023032716494059587_j_anona-2022-0291_ref_001
2023032716494059587_j_anona-2022-0291_ref_023
2023032716494059587_j_anona-2022-0291_ref_002
2023032716494059587_j_anona-2022-0291_ref_024
2023032716494059587_j_anona-2022-0291_ref_021
2023032716494059587_j_anona-2022-0291_ref_022
2023032716494059587_j_anona-2022-0291_ref_020
2023032716494059587_j_anona-2022-0291_ref_009
2023032716494059587_j_anona-2022-0291_ref_007
2023032716494059587_j_anona-2022-0291_ref_008
2023032716494059587_j_anona-2022-0291_ref_005
2023032716494059587_j_anona-2022-0291_ref_006
2023032716494059587_j_anona-2022-0291_ref_003
2023032716494059587_j_anona-2022-0291_ref_025
2023032716494059587_j_anona-2022-0291_ref_004
2023032716494059587_j_anona-2022-0291_ref_012
2023032716494059587_j_anona-2022-0291_ref_013
2023032716494059587_j_anona-2022-0291_ref_010
2023032716494059587_j_anona-2022-0291_ref_011
2023032716494059587_j_anona-2022-0291_ref_018
2023032716494059587_j_anona-2022-0291_ref_019
2023032716494059587_j_anona-2022-0291_ref_016
2023032716494059587_j_anona-2022-0291_ref_017
2023032716494059587_j_anona-2022-0291_ref_014
2023032716494059587_j_anona-2022-0291_ref_015
References_xml – ident: 2023032716494059587_j_anona-2022-0291_ref_022
  doi: 10.1016/j.jde.2020.05.016
– ident: 2023032716494059587_j_anona-2022-0291_ref_024
  doi: 10.1137/21M1463136
– ident: 2023032716494059587_j_anona-2022-0291_ref_004
  doi: 10.1007/s00220-017-2866-1
– ident: 2023032716494059587_j_anona-2022-0291_ref_019
  doi: 10.1080/03605308908820654
– ident: 2023032716494059587_j_anona-2022-0291_ref_010
– ident: 2023032716494059587_j_anona-2022-0291_ref_008
  doi: 10.1016/j.anihpc.2008.06.001
– ident: 2023032716494059587_j_anona-2022-0291_ref_016
  doi: 10.1016/S0362-546X(96)00021-1
– ident: 2023032716494059587_j_anona-2022-0291_ref_013
  doi: 10.1016/j.na.2016.10.002
– ident: 2023032716494059587_j_anona-2022-0291_ref_021
  doi: 10.1512/iumj.2000.49.1893
– ident: 2023032716494059587_j_anona-2022-0291_ref_025
  doi: 10.1007/PL00001512
– ident: 2023032716494059587_j_anona-2022-0291_ref_005
  doi: 10.1137/15M1015959
– ident: 2023032716494059587_j_anona-2022-0291_ref_003
  doi: 10.1016/j.jfa.2017.01.025
– ident: 2023032716494059587_j_anona-2022-0291_ref_011
– ident: 2023032716494059587_j_anona-2022-0291_ref_009
  doi: 10.1007/s002050050163
– ident: 2023032716494059587_j_anona-2022-0291_ref_006
  doi: 10.1137/050624522
– ident: 2023032716494059587_j_anona-2022-0291_ref_012
  doi: 10.1063/1.1703944
– ident: 2023032716494059587_j_anona-2022-0291_ref_020
– ident: 2023032716494059587_j_anona-2022-0291_ref_018
  doi: 10.1080/03605309308820960
– ident: 2023032716494059587_j_anona-2022-0291_ref_001
  doi: 10.1007/s00030-008-7021-4
– ident: 2023032716494059587_j_anona-2022-0291_ref_002
  doi: 10.1016/j.na.2005.09.035
– ident: 2023032716494059587_j_anona-2022-0291_ref_017
  doi: 10.1007/BF00251502
– ident: 2023032716494059587_j_anona-2022-0291_ref_023
  doi: 10.1007/s43034-020-00101-w
– ident: 2023032716494059587_j_anona-2022-0291_ref_015
  doi: 10.1016/j.anihpc.2015.01.005
– ident: 2023032716494059587_j_anona-2022-0291_ref_014
  doi: 10.1007/s11005-013-0667-9
– ident: 2023032716494059587_j_anona-2022-0291_ref_007
  doi: 10.1137/19M1243907
SSID ssj0000851770
Score 2.4005673
Snippet In this article, we are concerned with normalized solutions for the -Laplacian equation with a trapping potential and -supercritical growth, where or The...
In this article, we are concerned with normalized solutions for the p p -Laplacian equation with a trapping potential and L r {L}^{r} -supercritical growth,...
In this article, we are concerned with normalized solutions for the pp -Laplacian equation with a trapping potential and Lr{L}^{r}-supercritical growth, where...
SourceID doaj
crossref
walterdegruyter
SourceType Open Website
Enrichment Source
Index Database
Publisher
StartPage 457
SubjectTerms 35J20
35J60
35J92
Laplacian equation
normalized solutions
p-laplacian equation
variational methods
Title Normalized solutions for the p-Laplacian equation with a trapping potential
URI https://www.degruyter.com/doi/10.1515/anona-2022-0291
https://doaj.org/article/18fa765190a24a8c9a5895bab5311284
Volume 12
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELYQEx0qnqK85IGBJTR2nDgZAVFVPDpRqZt1dhwEqqCUVAh-PXdJWhWkioU1cuTou7PvO_vyHWOnFMORVkOQxyIJFK6mAESsA5AuxXibZ97Secf9IOkP1c0oHi21-qKasFoeuAauK9ICdII8IwSpIHUZxGkWW7DoPLS30u6LMW8pmXquq6-E1mGj5YMxuwuYTQP6BOZeoczEjzBUqfW3WPujuqHO_eN09lnOb0SrQNPbZO2GIfKL-su22Jp_2WatJd3AHXY7IKY5fvryOV_4Dkf6yZHO8UlwB1RqhYbn_q2W8uZ03sqBl1MgQYZHPnktqU4Ixrts2Lt-uOoHTVeEwCGZKOk3KWkVZgleFsg5bRbiHlFY5GlOgYgAfFKoCIoodTJPRaIj5GyRKyCMijy0Ltpj64iF32c81h4JhfZeYF6ShSlgLqMQZZd5qRD3Djufg2RcIxlOnSvGhlIHRNVUqBpC1RCqHXa2eGFSq2WsHnpJqC-Gkcx19QCNbxrjm7-M32HRL5uZZgm-r5pXSHHwH1Mfsg3qPE_laFIfsfVyOvPHyE9Ke1K54jcJIuEV
linkProvider Directory of Open Access Journals
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ07T8MwEMdPUAbogHiK8vTAwBIaO-8REFCglAGQ2KyL4xSkQktJheDTc9eGCBAsrJGtWGc797vL-W-AXfbhhNXoZIEMHZ92k4MyiBxUJiZ_myU25XzHZSds3frnd8HdFBx9noXhssrMdoejt2KikNrM-mbEibJKa4A8cBMpNkaaYYqkXJXI5n3x2JuGmZDwP67BzEHr9PqqSrUwVUSRWwr7_NL9m08aS_fXYf51_Lu6GssXr3OyAPMlLoqDyfwuwpR9WoL6FxHBZbjoMHb2Ht5tJqqFJIhFBbGdGDht5LorWgXCPk90vQUnXwWKYoisztAVg37BRUPYW4Hbk-Obo5ZTXpHgGCKLgs9MqdSnkMGqnAA0TVz6YOQpQZvxUXqINsx9D3MvNiqLZRh5BHCeydH18sxNjbcKNbKFXQMRRJboIrJWUpCSuDFSYOMrH01ilR_n2ID9TyNpU-qH8zUWPc1xBFlVj62q2aqardqAvarDYCKd8XfTQ7Z61Yw1r8cP-sOuLreQljSIKCTidJGGFZsEgzgJUkzpM8JetgHejznT5X58-eu9Usn1f_XagdnWzWVbt886Fxswx3fQc2GaijahVgxHdotIpUi3y5X4Ada45cI
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LTxsxEB5BkBAcEJRWpOXhQw9ctlk_9nWkQAiPBiRA4mbNer0RUkTSdKOq_PrOJNtVQOXCdWXL1uex55vZ8WeAr-zDiVZjUEQyDgztpgBllASoXEr-tsh8zvmOH_24d28uHqKHhbswXFZZ-MFk-qeaK6R2ipGbcqKs0RogD9xBio2RVpgiqVBlsjMuymVYieNMmxasHPXObq-bTAuTiiQJa12f__R-4ZJmyv3rsPF79re6mcqC0-luwkbNFsXRfHm3YMk_fYD1BQ3BbbjsM-scPj77QjR2JIiKCqJ2YhxcIZddkREI_3Mu6y049ypQVBNkcYaBGI8qrhnC4Ue4757eHfeC-oWEwBGxqPjKlMoNRQxelcQ_8yyk86LMibM5g1Ij-rg0GkudOlWkMk408TftSgx1WYS505-gRVj4HRBR4olcJN5LilGyMEWKa4wy6DKvTFpiG779A8m6Wj6cX7EYWg4jCFU7Q9UyqpZRbcNh02E8V854u-l3Rr1pxpLXsw-jycDWO8hKmkQSE-EMkaaVugyjNItyzOkUYSfbBv1qzWy9HX-9Na5U8vO7eh3A6s1J116d9y-_wBq_QM9laSrZhVY1mfo94ilVvl8b4l-Bj-To
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+solutions+for+the+p-Laplacian+equation+with+a+trapping+potential&rft.jtitle=Advances+in+nonlinear+analysis&rft.au=Wang+Chao&rft.au=Sun+Juntao&rft.date=2023-03-27&rft.pub=De+Gruyter&rft.eissn=2191-950X&rft.volume=12&rft.issue=1&rft.spage=457&rft.epage=472&rft_id=info:doi/10.1515%2Fanona-2022-0291&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_18fa765190a24a8c9a5895bab5311284
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2191-950X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2191-950X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2191-950X&client=summon