Existence and multiplicity of solutions for Klein–Gordon–Maxwell systems with sign-changing potentials View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-12

AUTHORS

Chongqing Wei, Anran Li

ABSTRACT

In this paper, we study the following nonlinear Klein–Gordon–Maxwell system: {−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+λh(x)|u|q−2u,x∈R3,Δϕ=(ω+ϕ)u2,x∈R3,(Pλ) where ω and λ are positive constants, V is a continuous function with negative infimum, q∈(1,2), h∈L22−q(R3) is a positive potential function. Under the classic Ambrosetti–Rabinowitz condition, nontrivial solutions are obtained via the symmetric mountain pass theorem and the mountain pass theorem. In our paper, the nonlinearity F can also change sign and does not need to satisfy any 4-superlinear condition. We extend and improve some existing results to some extent. More... »

PAGES

72

References to SciGraph publications

  • 2010-10. Multiple solutions for nonhomogeneous Schrödinger–Maxwell and Klein– Gordon–Maxwell equations on R3 in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • 2014-04. Multiplicity of Solutions for a Nonlinear Klein-Gordon-Maxwell System in ACTA APPLICANDAE MATHEMATICAE
  • 2014-01. On perturbation of a functional with the mountain pass geometry in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1186/s13662-019-2020-9

    DOI

    http://dx.doi.org/10.1186/s13662-019-2020-9

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112396689


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1117", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Public Health and Health Services", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/11", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Medical and Health Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Shanxi University", 
              "id": "https://www.grid.ac/institutes/grid.163032.5", 
              "name": [
                "School of Mathematical Sciences, Shanxi University, Taiyuan, People\u2019s Republic of China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Wei", 
            "givenName": "Chongqing", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Shanxi University", 
              "id": "https://www.grid.ac/institutes/grid.163032.5", 
              "name": [
                "School of Mathematical Sciences, Shanxi University, Taiyuan, People\u2019s Republic of China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Li", 
            "givenName": "Anran", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s00030-010-0068-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001660468", 
              "https://doi.org/10.1007/s00030-010-0068-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00030-010-0068-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001660468", 
              "https://doi.org/10.1007/s00030-010-0068-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2011.04.050", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014639620"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s1874-5733(05)80009-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015414589"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2003.05.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015555359"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10440-013-9845-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016295527", 
              "https://doi.org/10.1007/s10440-013-9845-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0362-546x(01)00688-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017620603"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2012.02.023", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020137992"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2010.09.033", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020208586"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.camwa.2014.07.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030539117"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.nonrwa.2014.09.006", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030610599"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-1236(73)90051-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032792397"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2014.07.019", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033670666"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0362-546x(83)90115-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036959656"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.anihpc.2010.02.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039978846"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00526-013-0595-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052884695", 
              "https://doi.org/10.1007/s00526-013-0595-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s030821050000353x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054892579"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s030821050000353x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054892579"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0308210509001814", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054895340"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0129055x02001168", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062897916"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/ans-2004-0305", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1067520456"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/cpaa.2011.10.709", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071731804"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/dcds.2012.32.2271", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071734456"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-12", 
        "datePublishedReg": "2019-12-01", 
        "description": "In this paper, we study the following nonlinear Klein\u2013Gordon\u2013Maxwell system: {\u2212\u0394u+V(x)u\u2212(2\u03c9+\u03d5)\u03d5u=f(x,u)+\u03bbh(x)|u|q\u22122u,x\u2208R3,\u0394\u03d5=(\u03c9+\u03d5)u2,x\u2208R3,(P\u03bb) where \u03c9 and \u03bb are positive constants, V is a continuous function with negative infimum, q\u2208(1,2), h\u2208L22\u2212q(R3) is a positive potential function. Under the classic Ambrosetti\u2013Rabinowitz condition, nontrivial solutions are obtained via the symmetric mountain pass theorem and the mountain pass theorem. In our paper, the nonlinearity F can also change sign and does not need to satisfy any 4-superlinear condition. We extend and improve some existing results to some extent.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1186/s13662-019-2020-9", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1052613", 
            "issn": [
              "1687-1839", 
              "1687-1847"
            ], 
            "name": "Advances in Difference Equations", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2019"
          }
        ], 
        "name": "Existence and multiplicity of solutions for Klein\u2013Gordon\u2013Maxwell systems with sign-changing potentials", 
        "pagination": "72", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "d424ac43e4f919a440e8dba66b999c2781a56c88ca6c8f7da46a59198ce80d54"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1186/s13662-019-2020-9"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1112396689"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1186/s13662-019-2020-9", 
          "https://app.dimensions.ai/details/publication/pub.1112396689"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T10:04", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000347_0000000347/records_89826_00000004.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1186%2Fs13662-019-2020-9"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1186/s13662-019-2020-9'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/s13662-019-2020-9'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/s13662-019-2020-9'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/s13662-019-2020-9'


     

    This table displays all metadata directly associated to this object as RDF triples.

    132 TRIPLES      21 PREDICATES      48 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1186/s13662-019-2020-9 schema:about anzsrc-for:11
    2 anzsrc-for:1117
    3 schema:author N523151906ca84bb68b3d9660c9fd9fb4
    4 schema:citation sg:pub.10.1007/s00030-010-0068-z
    5 sg:pub.10.1007/s00526-013-0595-7
    6 sg:pub.10.1007/s10440-013-9845-0
    7 https://doi.org/10.1016/0022-1236(73)90051-7
    8 https://doi.org/10.1016/0362-546x(83)90115-3
    9 https://doi.org/10.1016/j.anihpc.2010.02.001
    10 https://doi.org/10.1016/j.camwa.2014.07.001
    11 https://doi.org/10.1016/j.na.2003.05.001
    12 https://doi.org/10.1016/j.na.2010.09.033
    13 https://doi.org/10.1016/j.na.2011.04.050
    14 https://doi.org/10.1016/j.na.2012.02.023
    15 https://doi.org/10.1016/j.na.2014.07.019
    16 https://doi.org/10.1016/j.nonrwa.2014.09.006
    17 https://doi.org/10.1016/s0362-546x(01)00688-5
    18 https://doi.org/10.1016/s1874-5733(05)80009-9
    19 https://doi.org/10.1017/s030821050000353x
    20 https://doi.org/10.1017/s0308210509001814
    21 https://doi.org/10.1142/s0129055x02001168
    22 https://doi.org/10.1515/ans-2004-0305
    23 https://doi.org/10.3934/cpaa.2011.10.709
    24 https://doi.org/10.3934/dcds.2012.32.2271
    25 schema:datePublished 2019-12
    26 schema:datePublishedReg 2019-12-01
    27 schema:description In this paper, we study the following nonlinear Klein–Gordon–Maxwell system: {−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+λh(x)|u|q−2u,x∈R3,Δϕ=(ω+ϕ)u2,x∈R3,(Pλ) where ω and λ are positive constants, V is a continuous function with negative infimum, q∈(1,2), h∈L22−q(R3) is a positive potential function. Under the classic Ambrosetti–Rabinowitz condition, nontrivial solutions are obtained via the symmetric mountain pass theorem and the mountain pass theorem. In our paper, the nonlinearity F can also change sign and does not need to satisfy any 4-superlinear condition. We extend and improve some existing results to some extent.
    28 schema:genre research_article
    29 schema:inLanguage en
    30 schema:isAccessibleForFree true
    31 schema:isPartOf N5e69c5758ba942e18531534907eac955
    32 Na510cb9d0469407d8c04f263dbb655d0
    33 sg:journal.1052613
    34 schema:name Existence and multiplicity of solutions for Klein–Gordon–Maxwell systems with sign-changing potentials
    35 schema:pagination 72
    36 schema:productId N55c29756ad5a4800b12b1bc3024b4283
    37 Nb2d7a2e36c984ffeac2206ae67817279
    38 Nc3ad874ffdbf436d986991f5825511fa
    39 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112396689
    40 https://doi.org/10.1186/s13662-019-2020-9
    41 schema:sdDatePublished 2019-04-11T10:04
    42 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    43 schema:sdPublisher N31bc75f2bf4d42d6a950ebb386aa085b
    44 schema:url https://link.springer.com/10.1186%2Fs13662-019-2020-9
    45 sgo:license sg:explorer/license/
    46 sgo:sdDataset articles
    47 rdf:type schema:ScholarlyArticle
    48 N0aab00c08e0f419099b0b15ddc11621d schema:affiliation https://www.grid.ac/institutes/grid.163032.5
    49 schema:familyName Wei
    50 schema:givenName Chongqing
    51 rdf:type schema:Person
    52 N31bc75f2bf4d42d6a950ebb386aa085b schema:name Springer Nature - SN SciGraph project
    53 rdf:type schema:Organization
    54 N523151906ca84bb68b3d9660c9fd9fb4 rdf:first N0aab00c08e0f419099b0b15ddc11621d
    55 rdf:rest N827c4c53c4a44857a392442b80d61b49
    56 N55c29756ad5a4800b12b1bc3024b4283 schema:name dimensions_id
    57 schema:value pub.1112396689
    58 rdf:type schema:PropertyValue
    59 N5e69c5758ba942e18531534907eac955 schema:volumeNumber 2019
    60 rdf:type schema:PublicationVolume
    61 N655290df112c4bcea09656532d797f85 schema:affiliation https://www.grid.ac/institutes/grid.163032.5
    62 schema:familyName Li
    63 schema:givenName Anran
    64 rdf:type schema:Person
    65 N827c4c53c4a44857a392442b80d61b49 rdf:first N655290df112c4bcea09656532d797f85
    66 rdf:rest rdf:nil
    67 Na510cb9d0469407d8c04f263dbb655d0 schema:issueNumber 1
    68 rdf:type schema:PublicationIssue
    69 Nb2d7a2e36c984ffeac2206ae67817279 schema:name readcube_id
    70 schema:value d424ac43e4f919a440e8dba66b999c2781a56c88ca6c8f7da46a59198ce80d54
    71 rdf:type schema:PropertyValue
    72 Nc3ad874ffdbf436d986991f5825511fa schema:name doi
    73 schema:value 10.1186/s13662-019-2020-9
    74 rdf:type schema:PropertyValue
    75 anzsrc-for:11 schema:inDefinedTermSet anzsrc-for:
    76 schema:name Medical and Health Sciences
    77 rdf:type schema:DefinedTerm
    78 anzsrc-for:1117 schema:inDefinedTermSet anzsrc-for:
    79 schema:name Public Health and Health Services
    80 rdf:type schema:DefinedTerm
    81 sg:journal.1052613 schema:issn 1687-1839
    82 1687-1847
    83 schema:name Advances in Difference Equations
    84 rdf:type schema:Periodical
    85 sg:pub.10.1007/s00030-010-0068-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1001660468
    86 https://doi.org/10.1007/s00030-010-0068-z
    87 rdf:type schema:CreativeWork
    88 sg:pub.10.1007/s00526-013-0595-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052884695
    89 https://doi.org/10.1007/s00526-013-0595-7
    90 rdf:type schema:CreativeWork
    91 sg:pub.10.1007/s10440-013-9845-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016295527
    92 https://doi.org/10.1007/s10440-013-9845-0
    93 rdf:type schema:CreativeWork
    94 https://doi.org/10.1016/0022-1236(73)90051-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032792397
    95 rdf:type schema:CreativeWork
    96 https://doi.org/10.1016/0362-546x(83)90115-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036959656
    97 rdf:type schema:CreativeWork
    98 https://doi.org/10.1016/j.anihpc.2010.02.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039978846
    99 rdf:type schema:CreativeWork
    100 https://doi.org/10.1016/j.camwa.2014.07.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030539117
    101 rdf:type schema:CreativeWork
    102 https://doi.org/10.1016/j.na.2003.05.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015555359
    103 rdf:type schema:CreativeWork
    104 https://doi.org/10.1016/j.na.2010.09.033 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020208586
    105 rdf:type schema:CreativeWork
    106 https://doi.org/10.1016/j.na.2011.04.050 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014639620
    107 rdf:type schema:CreativeWork
    108 https://doi.org/10.1016/j.na.2012.02.023 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020137992
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1016/j.na.2014.07.019 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033670666
    111 rdf:type schema:CreativeWork
    112 https://doi.org/10.1016/j.nonrwa.2014.09.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030610599
    113 rdf:type schema:CreativeWork
    114 https://doi.org/10.1016/s0362-546x(01)00688-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017620603
    115 rdf:type schema:CreativeWork
    116 https://doi.org/10.1016/s1874-5733(05)80009-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015414589
    117 rdf:type schema:CreativeWork
    118 https://doi.org/10.1017/s030821050000353x schema:sameAs https://app.dimensions.ai/details/publication/pub.1054892579
    119 rdf:type schema:CreativeWork
    120 https://doi.org/10.1017/s0308210509001814 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054895340
    121 rdf:type schema:CreativeWork
    122 https://doi.org/10.1142/s0129055x02001168 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062897916
    123 rdf:type schema:CreativeWork
    124 https://doi.org/10.1515/ans-2004-0305 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067520456
    125 rdf:type schema:CreativeWork
    126 https://doi.org/10.3934/cpaa.2011.10.709 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071731804
    127 rdf:type schema:CreativeWork
    128 https://doi.org/10.3934/dcds.2012.32.2271 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071734456
    129 rdf:type schema:CreativeWork
    130 https://www.grid.ac/institutes/grid.163032.5 schema:alternateName Shanxi University
    131 schema:name School of Mathematical Sciences, Shanxi University, Taiyuan, People’s Republic of China
    132 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...