{
  "abstract": "The purpose of this paper is to investigate the finite-order entire solutions of the following Fermat-type partial differential-difference equations: \\begin{align*} (P_1(z)f(z+c))^{m_1}+\\left(P_2(z)f(z)+\\sideset{}{_{j=1}^m}{\\sum} Q_j(z)\\partial_{z_j}(f(z))\\right)^{m_2}=P(z), \\end{align*} \\begin{align*} (P_1(z)f(z))^{m_1}+\\left(P_2(z)f(z+c)+\\sideset{}{_{j=1}^m}{\\sum} Q_j(z)\\partial_{z_j}(f(z))\\right)^{m_2}=P(z) \\end{align*} and \\begin{align*} \\left(\\sideset{}{_{j=1}^m}{\\sum} Q_j(z)\\partial_{z_j}(f(z))\\right)^{m_1}+\\left(P_1(z)f(z+c)+P_2(z)f(z)\\right)^{m_2}=P(z), \\end{align*} in $\\mathbb{C}^m$, where $m_1,m_2\\in\\mathbb{N}$ such that $m_1+m_2>2$, $c=(c_1,c_2,\\ldots,c_m)\\in\\mathbb{C}^m$, $P(\\not\\equiv 0)$, $P_1$, $P_2$ and $Q_i\\;(i=1,2,\\ldots,m)$ are polynomials in $\\mathbb{C}^m$ such that $P(z)$ is irreducible in $\\mathbb{C}^m$. The results established in this paper generalize those of Xu et al. \\cite{Xu-Luo-Cao-2025} from $\\mathbb{C}$ to $\\mathbb{C}^m$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01931",
  "author_total": 4,
  "authors": [
    {
      "name": "Sujoy Majumder"
    },
    {
      "name": "Jhilik Banerjee"
    },
    {
      "name": "Abhijit Banerjee"
    },
    {
      "name": "Elias Saleeby"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bt12rrvwkcgp4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01931",
  "fulltext_url": null,
  "id": "bt12rrvwkcgp4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01931",
  "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.CV"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bt12rrvwkcgp4.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Entire solutions of Fermat-Type Partial Differential-Difference equations in higher dimensions",
  "title_text": "Entire solutions of Fermat-Type Partial Differential-Difference equations in higher dimensions",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/bt12rrvwkcgp4",
  "venue": "arXiv",
  "versions": []
}