{
  "abstract": "We classify all positive classical solutions of the Lane--Emden system $$ -Δu=v^p \\, \\, \\text{in } \\, \\, \\mathbb{R}^N, \\, \\, -Δv=u^q \\, \\, \\text{in} \\, \\, \\mathbb{R}^N, $$ where $N\\geq3$ and $p,q>0$ satisfy $$ \\frac{1}{p+1}+\\frac{1}{q+1}=\\frac{N-2}{N}.$$Without assuming boundedness, decay at infinity, or finite energy, we prove that every such solution has the form $$ u(x)=λ^{\\frac{N}{q+1}}U(λ(x-a)), \\, \\, v(x)=λ^{\\frac{N}{p+1}}V(λ(x-a)), $$ for some $a\\in \\mathbb{R}^N$ and $λ>0$, where $(U,V)$ is the positive radial ground state centered at the origin and normalized by $U(0)=1$. Consequently, both components are radially symmetric about the same point and satisfy $$ \\int_{\\mathbb{R}^N}u^{q+1}\\, dx = \\int_{\\mathbb{R}^N}v^{p+1}\\,dx<\\infty. $$ Our result extends the classical classification of positive solutions of the critical Sobolev equation by Caffarelli, Gidas and Spruck and Chen and Li to the critical Lane-Emden system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27875",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuxia Guo"
    },
    {
      "name": "Yichen Hu"
    },
    {
      "name": "Shaolong Peng"
    },
    {
      "name": "Tingfeng Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fx2540f57dhzr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27875",
  "fulltext_url": null,
  "id": "fx2540f57dhzr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27875",
  "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": "W7223093274",
  "pdf_url": "https://arxiv.org/pdf/2610.27875",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fx2540f57dhzr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27875",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27875"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Classification of positive solutions to the critical Lane-Emden system",
  "title_text": "Classification of positive solutions to the critical Lane-Emden system",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/fx2540f57dhzr",
  "venue": "arXiv",
  "versions": []
}