{
  "abstract": "In this paper, we study the asymptotic behavior of least energy solutions to Lane--Emden problems on compact metric graphs as $p \\to \\infty$. For the problem with Dirichlet--Kirchhoff boundary conditions, we characterize the limiting variational problem in terms of the Dirichlet--Kirchhoff Green function and show that least energy positive solutions converge, up to a subsequence, to a normalized Green function centered at a maximizer of the diagonal Green function. We also show that their maximum points approach the set of such maximizers. For the problem with Kirchhoff--Neumann boundary conditions, we characterize the limiting variational problem on compact metric graphs without cycles and show that least energy solutions converge, up to a subsequence, to a limiting profile associated with a pair of points realizing the maximal distance on the graph. Moreover, the distance between their maximum and minimum points converges to the maximal distance on the graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15486",
  "author_total": 1,
  "authors": [
    {
      "name": "Kazuki Sato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2v6eb2rhd4pnq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15486",
  "fulltext_url": null,
  "id": "2v6eb2rhd4pnq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15486",
  "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": "W7213350430",
  "pdf_url": "https://arxiv.org/pdf/2609.15486",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2v6eb2rhd4pnq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15486",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15486"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic Behavior of Least Energy Solutions to the Lane--Emden Problem on Metric Graphs",
  "title_text": "Asymptotic Behavior of Least Energy Solutions to the Lane--Emden Problem on Metric Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/2v6eb2rhd4pnq",
  "venue": "arXiv",
  "versions": []
}