{
  "abstract": "This paper is concerned with the following planar Schrodinger-Poisson system: $\\begin{cases} -Δu +V(x)u+λϕu=u\\ln u^2, & \\text{in }{R}^2,\\\\ Δϕ=u^2, & \\text{in }{R}^2. \\end{cases}$ where $λ\\in{R}$ is a parameter and $V\\in C^1({R}^2,R}^{+})$ is a coercive potential. Due to the presence of the logarithmic nonlinearity, the manifold method developed by Ruiz [R] is not applicable here. We apply a general minimax principle to an auxiliary functional and prove the existence of a nontrivial solution. Then, by minimizing the energy functional over the set of all nontrivial solutions, we succeed in showing that the system admits a ground state solution. If, in addition, $V$ is radially symmetric, we obtain infinitely many non radial sign-changing solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24043",
  "author_total": 3,
  "authors": [
    {
      "name": "Wei Long"
    },
    {
      "name": "Changchang Yan"
    },
    {
      "name": "Jianghua Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zkn43f5mxzr5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24043",
  "fulltext_url": null,
  "id": "9zkn43f5mxzr5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24043",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7214032828",
  "pdf_url": "https://arxiv.org/pdf/2609.24043",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zkn43f5mxzr5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24043",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24043"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Multiple solutions for planar Schrodinger-Poisson system with logarithmic nonlinearity",
  "title_text": "Multiple solutions for planar Schrodinger-Poisson system with logarithmic nonlinearity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9zkn43f5mxzr5",
  "venue": "arXiv",
  "versions": []
}