{
  "abstract": "In this paper, we study sign-changing normalized solutions of the Kirchhoff problem \\[ \\begin{cases} -\\left(a+b\\displaystyle\\int_Ω|\\nabla u|^2\\,dx\\right)Δu =|u|^{p-2}u+μu &\\text{in }Ω,\\\\ u=0 &\\text{on }\\partialΩ, \\end{cases} \\] subject to the constraint \\[ \\int_Ω|u|^2\\,dx=c, \\] where $a,b>0$, $Ω\\subset\\mathbb R^N$ is a smooth bounded connected domain, $1\\le N\\le3$, $c>0$ is prescribed, and $μ\\in\\mathbb R$ is a Lagrange multiplier. We assume $2<p<\\infty$ for $N=1,2$ and $2<p\\le6$ for $N=3$. For every integer $k\\ge1$, we obtain at least $k$ distinct pairs of sign-changing normalized solutions for sufficiently small $c>0$. We determine the small mass asymptotics of their energies, Lagrange multipliers, and rescaled profiles in terms of the distinct Dirichlet eigenvalues and their eigenspaces. When $2<p<2+\\frac{8}{N}$, we obtain infinitely many such pairs for every prescribed mass $c>0$, with energies tending to $+\\infty$. At $p=2+\\frac{8}{N}$, this conclusion holds for every sufficiently small fixed mass. We also establish the existence of a least energy sign-changing normalized solution on general bounded domains for every prescribed mass when $2<p<2+\\frac{8}{N}$. For sufficiently small mass, such a solution exists on general bounded domains when $p=2+\\frac{8}{N}$ and on star-shaped domains when $p>2+\\frac{8}{N}$. For any family of such least energy solutions, the rescaled profiles approach the $L^2$-unit sphere of the second Dirichlet eigenspace in $H_0^1(Ω)$ as $c\\to0^+$. The finite multiplicity and least energy results include the Sobolev critical case $N=3$, $p=6$. The proofs combine a localized symmetric minimax construction, energy comparisons with one-signed critical points, and compactness arguments that preserve the sign-changing property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07199",
  "author_total": 2,
  "authors": [
    {
      "name": "Qun Wang"
    },
    {
      "name": "Xiaojun Chang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wcwc91g3kftz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07199",
  "fulltext_url": null,
  "id": "1wcwc91g3kftz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07199",
  "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/2611.07199",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1wcwc91g3kftz.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07199",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07199"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Multiplicity and least energy sign-changing normalized solutions for a Kirchhoff equation on bounded domains",
  "title_text": "Multiplicity and least energy sign-changing normalized solutions for a Kirchhoff equation on bounded domains",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/1wcwc91g3kftz",
  "venue": "arXiv",
  "versions": []
}