{
  "abstract": "We prove the existence of nonnegative radial ground states for a class of nonlinear biharmonic equations in $\\mathbb R^N$, covering subcritical and critical nonlinearities. The solutions are obtained as limits of clamped ground states on expanding balls. The Cassani-Tarsia homogeneous maximum principle in [D. Cassani. A. Tarsia, Adv. Nonlinear Anal. 11 (2022)] makes the approximating states positive. A variational decomposition on the radial Nehari manifold then excludes every zero sphere of positive radius, so the limiting ground state is positive on $\\mathbb R^N\\setminus\\{0\\}$. When the fourth order operator factorises into two second-order operators with positive resolvents, the conclusion upgrades to $u>0$ throughout $\\mathbb R^N$, including at the origin. We also give an explicit counterexample showing that the tempting extension of the homogeneous maximum principle to super-solutions with arbitrary nonhomogeneous boundary data is false, even with an arbitrarily large positive zeroth-order coefficient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11773",
  "author_total": 4,
  "authors": [
    {
      "name": "Daniele Cassani"
    },
    {
      "name": "Zhisu Liu"
    },
    {
      "name": "Giulio Romani"
    },
    {
      "name": "Antonio Tarsia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cctfhvbj2mb5x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11773",
  "fulltext_url": null,
  "id": "cctfhvbj2mb5x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11773",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7212224758",
  "pdf_url": "https://arxiv.org/pdf/2609.11773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cctfhvbj2mb5x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.11773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Positive radial ground states for nonlinear biharmonic equations: maximum principles and expanding-domain approximation",
  "title_text": "Positive radial ground states for nonlinear biharmonic equations: maximum principles and expanding-domain approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/cctfhvbj2mb5x",
  "venue": "arXiv",
  "versions": []
}