{
  "abstract": "We study the uniqueness of bound states for the following scalar field equation $$ -Δu+u=-\\varepsilon |u|^{q-1}u+|u|^{p-1}u \\,\\ \\ \\mbox{in}\\,\\ \\mathbb R^N, \\,\\ \\varepsilon>0,\\tag*{$(*)$} $$ where $ N\\ge3,\\ 1<p<(N+2)/(N-2)$ and $q>1$ satisfies $q \\neq p$. For each integer $k \\geq 1$, we prove that the equation $(*)$ has, up to translation and reflection, a unique bound state with precisely $k$ nodes in a natural coupling regime, where $\\varepsilon>0$ is sufficiently small. Our results address a conjecture of [H. Berestycki and P. L. Lions, ARMA, 1983][M. X. Tang, Invent. Math., 2026] on the uniqueness of fixed-node bound states for the equation $(*)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15232",
  "author_total": 3,
  "authors": [
    {
      "name": "Yujin Guo"
    },
    {
      "name": "Wei Ji"
    },
    {
      "name": "Yong Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xpd1cgs4yd34.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15232",
  "fulltext_url": null,
  "id": "9xpd1cgs4yd34",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15232",
  "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": "W7221766889",
  "pdf_url": "https://arxiv.org/pdf/2610.15232",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xpd1cgs4yd34.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15232",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15232"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniqueness of Bound States for Double-Power Scalar Field Equations",
  "title_text": "Uniqueness of Bound States for Double-Power Scalar Field Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9xpd1cgs4yd34",
  "venue": "arXiv",
  "versions": []
}