{
  "abstract": "We study radial bound states of \\[ Δu-\\abs{u}^{q-1}u+\\abs{u}^{p-1}u=0 \\quad\\text{in }\\R^n, \\qquad n\\ge3,\\qquad 1<q<p<\\frac{n+2}{n-2}. \\] For every integer $k\\ge1$, we prove that there is exactly one radial bound state with $k$ simple zeros and $u(0)>0$. Its absolute maximum is attained at the origin. This confirms the zero-mass, Sobolev-subcritical case of Tang's double-power uniqueness conjecture. The proof adapts Tang's phase-transition analysis and combines it with a finite-level separation argument inspired by Cortázar--García-Huidobro--Yarur. Three main difficulties arise in the zero-mass double-power setting: the sign changes of key comparison quantities in the low-amplitude region, the possible failure of pointwise positivity of an auxiliary quantity when $n=3$ and $p+q<3$, and the absence of exponential decay at infinity. We overcome these difficulties by introducing bridge functionals to propagate the required sign information through low amplitudes, establishing a weighted integral positivity estimate in the exceptional three-dimensional range, and combining a radial-flux tail estimate with finite-level inverse-branch comparison. We also establish the strict ordering of the bound-state shooting heights and show that the shooting variation along the \\(k\\)-node state has exactly \\(k+1\\) simple zeros.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15405",
  "author_total": 2,
  "authors": [
    {
      "name": "Wenjing Chen"
    },
    {
      "name": "Zexi Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tg30eavw5azs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15405",
  "fulltext_url": null,
  "id": "9tg30eavw5azs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15405",
  "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": "W7221806223",
  "pdf_url": "https://arxiv.org/pdf/2610.15405",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9tg30eavw5azs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15405",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15405"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniqueness of prescribed-node radial bound states for a zero-mass double-power equation",
  "title_text": "Uniqueness of prescribed-node radial bound states for a zero-mass double-power equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9tg30eavw5azs",
  "venue": "arXiv",
  "versions": []
}