{
  "abstract": "We consider the following singular Liouville equation $-Δv=λV(x)|x|^2e^v \\quad \\text{in } B_1, \\quad v=0 \\quad \\text{on } \\partial B_1, $ where $B_1\\subset\\mathbb R^2$ is the unit disk, $λ>0$ is a small parameter, and $V$ is a positive smooth function. We first prove a non-degeneracy result for the bubbling solutions constructed in \\cite{D-W-Z2026} by the local Pohozaev identities. Then we use this non-degeneracy result to establish the local uniqueness of bubbling solutions whose concentration parameters are sufficiently close.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34815",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuxia Guo"
    },
    {
      "name": "Jionghao Lv"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qe4jhvdcj0aw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34815",
  "fulltext_url": null,
  "id": "3qe4jhvdcj0aw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34815",
  "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": "W7214770990",
  "pdf_url": "https://arxiv.org/pdf/2609.34815",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qe4jhvdcj0aw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34815",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34815"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Non-degeneracy and local uniqueness of bubbling solutions for a singular Liouville equation",
  "title_text": "Non-degeneracy and local uniqueness of bubbling solutions for a singular Liouville equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/3qe4jhvdcj0aw",
  "venue": "arXiv",
  "versions": []
}