{
  "abstract": "We consider the Dirichlet problem for the Lorentz--Minkowski mean curvature operator in a radial setting, $$ -\\operatorname{div}\\left(\\frac{\\nabla u}{\\sqrt{1-|\\nabla u|^2}}\\right) = λu + μg(u) \\quad \\text{in } \\mathcal B_R, \\qquad u = 0 \\quad \\text{on } \\partial\\mathcal B_R, $$ on a ball of radius $R$ centered at the origin $\\mathcal B_R \\subset \\mathbb{R}^N$, where $λ, μ\\geq 0$ are parameters, and the nonlinearity $g$ satisfies suitable growth assumptions at zero. We first prove an a priori dichotomy for the asymptotic behaviour, as $μ\\to +\\infty$, of solutions with a prescribed number of zeros: either they converge uniformly to $0$, or they converge to a piecewise affine limit function $u_\\infty$, with $|u_\\infty'|=1$ a.e., having the same nodal properties. We then show that, when the number of zeros is appropriately prescribed, both alternatives are actually realized. More precisely, building on the multiplicity result in [A. Boscaggin, F. Colasuonno, and R. Ziegele, \\emph{Positive and nodal solutions for the Minkowski mean curvature equation: multiplicity and asymptotics}, arXiv:2607.15956 (2026)], we refine the shooting construction therein to obtain a family of small solutions converging to zero and, through a backward shooting argument, a family of large solutions converging to a saturated piecewise affine profile.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10166",
  "author_total": 3,
  "authors": [
    {
      "name": "Alberto Boscaggin"
    },
    {
      "name": "Francesca Colasuonno"
    },
    {
      "name": "Ricardo Ziegele"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9839m8ype7hde.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10166",
  "fulltext_url": null,
  "id": "9839m8ype7hde",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10166",
  "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"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221050785",
  "pdf_url": "https://arxiv.org/pdf/2610.10166",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9839m8ype7hde.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10166",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10166"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Collapse and saturation for radial nodal solutions of a Lorentz--Minkowski mean curvature equation",
  "title_text": "Collapse and saturation for radial nodal solutions of a Lorentz--Minkowski mean curvature equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/9839m8ype7hde",
  "venue": "arXiv",
  "versions": []
}