{
  "abstract": "In this paper, we study the following Schrödinger-Newton system with a vanishing magnetic potential and an electric potential \\begin{equation}\\label{0.1} \\left\\{ \\renewcommand{\\arraystretch}{1.25} \\begin{array}{ll} (-i\\nabla +A(x))^2u+V(x)u=Φu, \\ & x\\in\\mathbb{R}^3,\\\\ -ΔΦ=|u|^2, \\ & x\\in\\mathbb{R}^3, \\end{array} \\right. \\end{equation} where $i$ is the imaginary unit, $A:\\mathbb{R}^3\\to \\mathbb{R}^3$ is a continuous magnetic potential, and $V:\\mathbb{R}^3\\to \\mathbb{R}$ is a continuous electric potential. First, we show that the ground state energy of system with $A(x)\\equiv0$ and $V(x)\\equiv V_{\\infty}>0$ is isolated. Using this fact together with a global compactness lemma, a barycenter function, and Brouwer degree theory, we prove that under suitable conditions on $A$ and $V$, system admits either a ground state solution or a high energy solution. Interestingly, whether a ground state solution exists is significantly affected by the magnetic potential $A$ and the electric potential $V$. Furthermore, we provide sufficient conditions that guarantee the existence of a ground state solution, as well as conditions under which no ground state solution exists and a high energy solution appears instead.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17945",
  "author_total": 4,
  "authors": [
    {
      "name": "Liying Shan"
    },
    {
      "name": "Wei Shuai"
    },
    {
      "name": "Ping Yang"
    },
    {
      "name": "Jianghua Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cz70p4x881ght.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17945",
  "fulltext_url": null,
  "id": "cz70p4x881ght",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17945",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221760160",
  "pdf_url": "https://arxiv.org/pdf/2610.17945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cz70p4x881ght.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17945"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Existence of solution for Schrödinger-Newton system with vanishing magnetic potential",
  "title_text": "Existence of solution for Schrödinger-Newton system with vanishing magnetic potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/cz70p4x881ght",
  "venue": "arXiv",
  "versions": []
}