{
  "abstract": "We consider the Minkowski mean curvature equation $$ -\\operatorname{div}\\left(\\frac{\\nabla u}{\\sqrt{1-|\\nabla u|^2}}\\right) =λu+μh(x,u) \\quad \\text{in } Ω, \\quad \\mathcal B u = 0 \\quad \\text{on } \\partial Ω, $$ where $\\mathcal B \\in \\{ \\mathcal D, \\mathcal N \\}$ is a Dirichlet or Neumann boundary condition and $Ω$ is a smooth bounded domain, required to be convex in the Neumann case. Moreover, $λ, μ\\geq0$ are parameters, and $h(x,u)$ is odd with respect to $u$ and positive for $u > 0$. Using minmax methods in nonsmooth critical point theory, we prove that $λ>λ^\\mathcal B_k$ yields at least $k$ pairs of nontrivial solutions with negative energy for every $μ\\geq0$, where $λ_k^\\mathcal B$ are the corresponding Laplacian eigenvalues, indexed by $λ^\\mathcal B_0=0$. Moreover, if $H(x,u):=\\int_0^u h(x,t)\\,dt=o(u^2)$ as $u\\to0$, we prove that for $λ\\in[λ^\\mathcal B_k,λ^\\mathcal B_{k+1})$ and every $j\\geq\\max\\{1,k\\}$, sufficiently large $μ$ yields at least $2j-k$ distinct pairs of solutions: $j$ with negative energy and $j-k$ with positive energy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07963",
  "author_total": 2,
  "authors": [
    {
      "name": "Alberto Boscaggin"
    },
    {
      "name": "Ricardo Ziegele"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5tkrjawnt22tw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07963",
  "fulltext_url": null,
  "id": "5tkrjawnt22tw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07963",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07963",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5tkrjawnt22tw.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07963",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07963"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Multiplicity via symmetry for the Minkowski mean curvature equation: Dirichlet and Neumann problems",
  "title_text": "Multiplicity via symmetry for the Minkowski mean curvature equation: Dirichlet and Neumann problems",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:34Z",
  "url": "https://research.draconitic.com/paper/5tkrjawnt22tw",
  "venue": "arXiv",
  "versions": []
}