{
  "abstract": "Let $n\\geq 2$ and $k\\geq 1$ be integers. We study finite order meromorphic solutions of the nonlinear differential-difference equation \\begin{equation*} f^{n}(z)f'(z)+P_{d}(z,f)=p_{1}(z){\\rm e}^{α_{1}z^{k}}+p_{2}(z){\\rm e}^{α_{2}z^{k}}, \\end{equation*} where $P_{d}(z,f)\\not\\equiv 0$ is a difference polynomial in $f$ of degree $d\\leq n-1$ whose coefficients are small meromorphic functions with respect to $f$, $p_{1},~p_{2}$ are nonzero meromorphic functions with $T(r,p_{j})=o(r^{k})$, $j=1,2$, and $α_{1}\\neqα_{2}$ are nonzero constants. We prove that every such solution has order exactly $k$, and obtain sufficient conditions on $n,~d,~k$ for the equation to admit no finite order meromorphic solution with $N(r,\\frac{1}{f})=S(r,f)$. Our results extend the known ones from linear exponents $z$ to polynomial exponents $z^{k}$, and replace the linear difference polynomials with the degree restriction $d\\leq n-2$ assumed in the literature by general ones of degree $d\\leq n-1$. Examples show that the restrictions on $n$ and $d$ are sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38247",
  "author_total": 2,
  "authors": [
    {
      "name": "Minfeng Chen"
    },
    {
      "name": "Zongsheng Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7y2t5r82t6m4k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38247",
  "fulltext_url": null,
  "id": "7y2t5r82t6m4k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38247",
  "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/2610.38247",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7y2t5r82t6m4k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38247",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38247"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Meromorphic solutions of a nonlinear differential-difference equation with two exponential terms",
  "title_text": "Meromorphic solutions of a nonlinear differential-difference equation with two exponential terms",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7y2t5r82t6m4k",
  "venue": "arXiv",
  "versions": []
}