Weighted Choquard Equation Perturbed with Weighted Nonlocal Term View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2021-08-03

AUTHORS

Gurpreet Singh

ABSTRACT

We investigate the following problem -div(v(x)|∇u|m-2∇u)+V(x)|u|m-2u=|x|-θ∗|u|b|x|α|u|b-2|x|αu+λ|x|-γ∗|u|c|x|β|u|c-2|x|βuinRN,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\mathrm{div}(v(x)|\nabla u|^{m-2}\nabla u)+V(x)|u|^{m-2}u= \left( |x|^{-\theta }*\frac{|u|^{b}}{|x|^{\alpha }}\right) \frac{|u|^{b-2}}{|x|^{\alpha }}u+\lambda \left( |x|^{-\gamma }*\frac{|u|^{c}}{|x|^{\beta }}\right) \frac{|u|^{c-2}}{|x|^{\beta }}u \quad \text { in }{\mathbb {R}}^{N}, \end{aligned}$$\end{document}where b,c,α,β>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b, c, \alpha , \beta >0$$\end{document}, θ,γ∈(0,N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta ,\gamma \in (0,N)$$\end{document}, N≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\ge 3$$\end{document}, 2≤m<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\le m< \infty$$\end{document} and λ∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda \in {\mathbb {R}}$$\end{document}. Here, we are concerned with the existence of groundstate solutions and least energy sign-changing solutions and that will be done by using the minimization techniques on the associated Nehari manifold and the Nehari nodal set respectively. More... »

PAGES

1-21

References to SciGraph publications

  • 2020-06-05. Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity in MEDITERRANEAN JOURNAL OF MATHEMATICS
  • 2007-04-30. Problem with Critical Sobolev Exponent and with Weight in CHINESE ANNALS OF MATHEMATICS, SERIES B
  • 2016-12-05. Choquard equations under confining external potentials in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • 2016-11-17. A guide to the Choquard equation in JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
  • 1996-05. On Gravity's role in Quantum State Reduction in GENERAL RELATIVITY AND GRAVITATION
  • 2007. Measure Theory in NONE
  • 2009-09-10. Semilinear elliptic equations with singular nonlinearities in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s12591-021-00579-3

    DOI

    http://dx.doi.org/10.1007/s12591-021-00579-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1140157462


    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/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin, Ireland", 
              "id": "http://www.grid.ac/institutes/grid.15596.3e", 
              "name": [
                "School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin, Ireland"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Singh", 
            "givenName": "Gurpreet", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s11784-016-0373-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005452842", 
              "https://doi.org/10.1007/s11784-016-0373-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11401-005-0435-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038366024", 
              "https://doi.org/10.1007/s11401-005-0435-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00030-016-0424-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1042870610", 
              "https://doi.org/10.1007/s00030-016-0424-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-34514-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012306418", 
              "https://doi.org/10.1007/978-3-540-34514-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00009-020-01523-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1128254516", 
              "https://doi.org/10.1007/s00009-020-01523-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00526-009-0266-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1030467257", 
              "https://doi.org/10.1007/s00526-009-0266-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02105068", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015563001", 
              "https://doi.org/10.1007/bf02105068"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2021-08-03", 
        "datePublishedReg": "2021-08-03", 
        "description": "We investigate the following problem -div(v(x)|\u2207u|m-2\u2207u)+V(x)|u|m-2u=|x|-\u03b8\u2217|u|b|x|\u03b1|u|b-2|x|\u03b1u+\u03bb|x|-\u03b3\u2217|u|c|x|\u03b2|u|c-2|x|\u03b2uinRN,\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} -\\mathrm{div}(v(x)|\\nabla u|^{m-2}\\nabla u)+V(x)|u|^{m-2}u= \\left( |x|^{-\\theta }*\\frac{|u|^{b}}{|x|^{\\alpha }}\\right) \\frac{|u|^{b-2}}{|x|^{\\alpha }}u+\\lambda \\left( |x|^{-\\gamma }*\\frac{|u|^{c}}{|x|^{\\beta }}\\right) \\frac{|u|^{c-2}}{|x|^{\\beta }}u \\quad \\text { in }{\\mathbb {R}}^{N}, \\end{aligned}$$\\end{document}where b,c,\u03b1,\u03b2>0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$b, c, \\alpha , \\beta >0$$\\end{document}, \u03b8,\u03b3\u2208(0,N)\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\theta ,\\gamma \\in (0,N)$$\\end{document}, N\u22653\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$N\\ge 3$$\\end{document}, 2\u2264m<\u221e\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$2\\le m< \\infty$$\\end{document} and \u03bb\u2208R\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda \\in {\\mathbb {R}}$$\\end{document}. Here, we are concerned with the existence of groundstate solutions and least energy sign-changing solutions and that will be done by using the minimization techniques on the associated Nehari manifold and the Nehari nodal set respectively.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s12591-021-00579-3", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136107", 
            "issn": [
              "0971-3514", 
              "0974-6870"
            ], 
            "name": "Differential Equations and Dynamical Systems", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }
        ], 
        "keywords": [
          "nodal", 
          "technique", 
          "terms", 
          "problem", 
          "existence", 
          "perturbed", 
          "solution", 
          "minimization technique", 
          "Nehari manifold", 
          "manifold", 
          "nonlocal term", 
          "sign-changing solutions", 
          "least energy sign-changing solution"
        ], 
        "name": "Weighted Choquard Equation Perturbed with Weighted Nonlocal Term", 
        "pagination": "1-21", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1140157462"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s12591-021-00579-3"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s12591-021-00579-3", 
          "https://app.dimensions.ai/details/publication/pub.1140157462"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-05-20T07:39", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/article/article_908.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s12591-021-00579-3"
      }
    ]
     

    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.10.1007/s12591-021-00579-3'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s12591-021-00579-3'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12591-021-00579-3'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12591-021-00579-3'


     

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

    92 TRIPLES      22 PREDICATES      43 URIs      28 LITERALS      4 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s12591-021-00579-3 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N2dd74f53bfa540ab8fda76bafe70d5b0
    4 schema:citation sg:pub.10.1007/978-3-540-34514-5
    5 sg:pub.10.1007/bf02105068
    6 sg:pub.10.1007/s00009-020-01523-5
    7 sg:pub.10.1007/s00030-016-0424-8
    8 sg:pub.10.1007/s00526-009-0266-x
    9 sg:pub.10.1007/s11401-005-0435-y
    10 sg:pub.10.1007/s11784-016-0373-1
    11 schema:datePublished 2021-08-03
    12 schema:datePublishedReg 2021-08-03
    13 schema:description We investigate the following problem -div(v(x)|∇u|m-2∇u)+V(x)|u|m-2u=|x|-θ∗|u|b|x|α|u|b-2|x|αu+λ|x|-γ∗|u|c|x|β|u|c-2|x|βuinRN,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\mathrm{div}(v(x)|\nabla u|^{m-2}\nabla u)+V(x)|u|^{m-2}u= \left( |x|^{-\theta }*\frac{|u|^{b}}{|x|^{\alpha }}\right) \frac{|u|^{b-2}}{|x|^{\alpha }}u+\lambda \left( |x|^{-\gamma }*\frac{|u|^{c}}{|x|^{\beta }}\right) \frac{|u|^{c-2}}{|x|^{\beta }}u \quad \text { in }{\mathbb {R}}^{N}, \end{aligned}$$\end{document}where b,c,α,β>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b, c, \alpha , \beta >0$$\end{document}, θ,γ∈(0,N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta ,\gamma \in (0,N)$$\end{document}, N≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\ge 3$$\end{document}, 2≤m<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\le m< \infty$$\end{document} and λ∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda \in {\mathbb {R}}$$\end{document}. Here, we are concerned with the existence of groundstate solutions and least energy sign-changing solutions and that will be done by using the minimization techniques on the associated Nehari manifold and the Nehari nodal set respectively.
    14 schema:genre article
    15 schema:inLanguage en
    16 schema:isAccessibleForFree true
    17 schema:isPartOf sg:journal.1136107
    18 schema:keywords Nehari manifold
    19 existence
    20 least energy sign-changing solution
    21 manifold
    22 minimization technique
    23 nodal
    24 nonlocal term
    25 perturbed
    26 problem
    27 sign-changing solutions
    28 solution
    29 technique
    30 terms
    31 schema:name Weighted Choquard Equation Perturbed with Weighted Nonlocal Term
    32 schema:pagination 1-21
    33 schema:productId Naae030ae6ac1411f81c9bae5763464f6
    34 Nd55fc9a1fce4419b8a3c2642b4e660fb
    35 schema:sameAs https://app.dimensions.ai/details/publication/pub.1140157462
    36 https://doi.org/10.1007/s12591-021-00579-3
    37 schema:sdDatePublished 2022-05-20T07:39
    38 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    39 schema:sdPublisher Nb2ca0e78f1c844b6abc39557ef0b2ac8
    40 schema:url https://doi.org/10.1007/s12591-021-00579-3
    41 sgo:license sg:explorer/license/
    42 sgo:sdDataset articles
    43 rdf:type schema:ScholarlyArticle
    44 N2dd74f53bfa540ab8fda76bafe70d5b0 rdf:first Nbe67ce4d3aa84f41a61569a23e69aafd
    45 rdf:rest rdf:nil
    46 Naae030ae6ac1411f81c9bae5763464f6 schema:name doi
    47 schema:value 10.1007/s12591-021-00579-3
    48 rdf:type schema:PropertyValue
    49 Nb2ca0e78f1c844b6abc39557ef0b2ac8 schema:name Springer Nature - SN SciGraph project
    50 rdf:type schema:Organization
    51 Nbe67ce4d3aa84f41a61569a23e69aafd schema:affiliation grid-institutes:grid.15596.3e
    52 schema:familyName Singh
    53 schema:givenName Gurpreet
    54 rdf:type schema:Person
    55 Nd55fc9a1fce4419b8a3c2642b4e660fb schema:name dimensions_id
    56 schema:value pub.1140157462
    57 rdf:type schema:PropertyValue
    58 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    59 schema:name Mathematical Sciences
    60 rdf:type schema:DefinedTerm
    61 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    62 schema:name Pure Mathematics
    63 rdf:type schema:DefinedTerm
    64 sg:journal.1136107 schema:issn 0971-3514
    65 0974-6870
    66 schema:name Differential Equations and Dynamical Systems
    67 schema:publisher Springer Nature
    68 rdf:type schema:Periodical
    69 sg:pub.10.1007/978-3-540-34514-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012306418
    70 https://doi.org/10.1007/978-3-540-34514-5
    71 rdf:type schema:CreativeWork
    72 sg:pub.10.1007/bf02105068 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015563001
    73 https://doi.org/10.1007/bf02105068
    74 rdf:type schema:CreativeWork
    75 sg:pub.10.1007/s00009-020-01523-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1128254516
    76 https://doi.org/10.1007/s00009-020-01523-5
    77 rdf:type schema:CreativeWork
    78 sg:pub.10.1007/s00030-016-0424-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042870610
    79 https://doi.org/10.1007/s00030-016-0424-8
    80 rdf:type schema:CreativeWork
    81 sg:pub.10.1007/s00526-009-0266-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1030467257
    82 https://doi.org/10.1007/s00526-009-0266-x
    83 rdf:type schema:CreativeWork
    84 sg:pub.10.1007/s11401-005-0435-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1038366024
    85 https://doi.org/10.1007/s11401-005-0435-y
    86 rdf:type schema:CreativeWork
    87 sg:pub.10.1007/s11784-016-0373-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005452842
    88 https://doi.org/10.1007/s11784-016-0373-1
    89 rdf:type schema:CreativeWork
    90 grid-institutes:grid.15596.3e schema:alternateName School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin, Ireland
    91 schema:name School of Mechanical and Manufacturing Engineering, Dublin City University, Dublin, Ireland
    92 rdf:type schema:Organization
     




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


    ...