{
  "abstract": "Let $Ω\\subset\\mathbb{R}^N$ be a bounded open connected set, and let $q\\in(1,2)$. We consider the sublinear $q$-eigenvalue problem for the Dirichlet Laplacian $-Δu=λ\\|u\\|_{L^q(Ω)}^{2-q}|u|^{q-2}u$, $u\\in H^1_0(Ω)\\setminus\\{0\\}$, whose first eigenvalue $λ_1(Ω)$ is simple, with eigenfunctions of constant sign. The definition of a second eigenvalue is not unique. Following the approach introduced by Molle and Passaseo for the linear Laplacian, we construct the first non-trivial curve of the corresponding Fučík spectrum, and show that it has a unique diagonal point $(γ(Ω),γ(Ω))$. The Fučík-selected second value $λ_2^F(Ω)=2^{1-\\frac{2}{q}}γ(Ω)$ is strictly larger than $λ_1(Ω)$, admits a two-phase variational characterisation, and satisfies a sharp Hong-Krahn-Szegő inequality: among sets of given measure it is minimised by the union of two equal balls. The selected solution at the diagonal point is a classical $(2,q)$-eigenfunction exactly when its nodal $L^q$-masses are balanced. We finally show that on balls in dimensions $N\\geq2$ every Fučík-selected solution is foliated Schwarz symmetric.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03971",
  "author_total": 3,
  "authors": [
    {
      "name": "Elie Alhelou"
    },
    {
      "name": "Gisella Croce"
    },
    {
      "name": "Giovanni Pisante"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fytj5dcdtamn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03971",
  "fulltext_url": null,
  "id": "fytj5dcdtamn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03971",
  "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/2611.03971",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fytj5dcdtamn9.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03971",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03971"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The first non-trivial Fučík curve for the sublinear Dirichlet Laplacian",
  "title_text": "The first non-trivial Fučík curve for the sublinear Dirichlet Laplacian",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:29Z",
  "url": "https://research.draconitic.com/paper/fytj5dcdtamn9",
  "venue": "arXiv",
  "versions": []
}