{
  "abstract": "For $n\\ge3$ and $γ>-1$, we study normal solutions of \\begin{equation*} (-Δ)^{n/2}u=(n-1)!\\,|x|^{nγ}e^{nu} \\quad\\hbox{in }\\R^n. \\end{equation*} We reformulate this problem on the cylinder via the Emden--Fowler transform. We first establish Kelvin symmetry for normal solutions. We then prove existence and uniqueness, up to dilation, of the radial normal solution and establish its radial nondegeneracy. Next, we carry out a detailed spectral analysis of the linearized operator and construct branches of nonradial normal solutions by the Crandall--Rabinowitz theorem. Finally, we prove that every normal solution is radial when $γ>0$ is sufficiently small.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11056",
  "author_total": 4,
  "authors": [
    {
      "name": "Haoyu Li"
    },
    {
      "name": "Tuoxin Li"
    },
    {
      "name": "Juncheng Wei"
    },
    {
      "name": "Wen Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fpwghjz3fa22c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11056",
  "fulltext_url": null,
  "id": "fpwghjz3fa22c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11056",
  "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": "W7221112668",
  "pdf_url": "https://arxiv.org/pdf/2610.11056",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fpwghjz3fa22c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11056",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11056"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniqueness and Symmetry Breaking for Singular $Q$-curvature Equations in $\\R^n$",
  "title_text": "Uniqueness and Symmetry Breaking for Singular Q-curvature Equations in R^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/fpwghjz3fa22c",
  "venue": "arXiv",
  "versions": []
}