{
  "abstract": "While superlinear discrete Kirchhoff problems have been extensively studied via variational minimax methods, the sublinear regime $\\sigma\\in(1,2)$, where the Kirchhoff energy dominates the reaction term, remains essentially unexplored. Also the asymptotic behavior of ground states as $\\lambda\\to0^+$ has not been investigated even in the continuous setting. We address this gap for the discrete Kirchhoff boundary value problem $$\\displaylines{ -m\\Big(\\sum_{j=0}^{N}|\\delta y_j|^2\\Big)\\Delta_d y_j =\\lambda h_j(y_j), \\quad j=1,\\ldots,N,\\cr y_0=y_{N+1}=0. }$$ Combining coercive minimization, constant-sign truncation, Krasnosel'skii genus theory, and scaling arguments, we establish existence of a nontrivial ground state for every $\\lambda >0$, two constant-sign solutions, and $N$ pairs of nontrivial solutions under an evenness assumption. We further derive the sharp scaling $\\inf\\mathcal J_\\lambda\\asymp-\\lambda^{\\frac{2}{2-\\sigma}}$, show that normalized ground states converge to minimizers of an explicit limit functional, and obtain, to our knowledge, the first quantitative convergence rate for this class of problems. Newton-continuation computations confirm the predicted scaling exponents to high precision.",
  "abstract_shown": true,
  "affiliations": [
    "Mohammed I Univ., Oujda, Morocco"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Mohammed Belahcen"
    },
    {
      "affs": [
        0
      ],
      "name": "Siham El Habib"
    },
    {
      "affs": [
        0
      ],
      "name": "Najib Tsouli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1v3e4nkfmzme6.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": "http://ejde.math.txstate.edu/Volumes/2026/77/abstr.html",
  "id": "1v3e4nkfmzme6",
  "issns": [
    "1072-6691"
  ],
  "landing_url": "http://ejde.math.txstate.edu/Volumes/2026/77/abstr.html",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ]
  ],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": "Texas State University",
  "ris": "https://research.draconitic.com/paper/1v3e4nkfmzme6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:09Z",
      "native_id": "b3c1bad2b24644008b8f3e01cac86a28",
      "source": "doaj",
      "url": "http://ejde.math.txstate.edu/Volumes/2026/77/abstr.html"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "lcc:QA1-939",
      "subfield": "general"
    }
  ],
  "title": "Ground state solutions and asymptotics for discrete Kirchhoff problems",
  "title_text": "Ground state solutions and asymptotics for discrete Kirchhoff problems",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:09Z",
  "url": "https://research.draconitic.com/paper/1v3e4nkfmzme6",
  "venue": "Electronic Journal of Differential Equations",
  "versions": []
}