{
  "abstract": "In this paper, we study the following linearly coupled Kirchhoff-Choquard system in $\\mathbb{R}^3$: \\begin{align*}\\left\\{\\begin{array}{l} &-\\left(a_1+b_1\\int_{\\mathbb{R}^3}|\\nabla u|^2\\,dx\\right)Δu+V_1(x)u=μ(I_α*|u|^p)|u|^{p-2}u+λv,\\quad x \\in \\mathbb{R}^3,\\cr &-\\left(a_2+b_2\\int_{\\mathbb{R}^3}|\\nabla v|^2\\,dx\\right)Δv+V_2(x)v=ν(I_α*|v|^q)|v|^{q-2}v+λu,\\quad x \\in \\mathbb{R}^3,\\cr &u, v \\in H^1(\\mathbb{R}^3), \\end{array}\\right. \\end{align*} where $a_1, a_2, b_1, b_2, λ, μ,$ and $ν$ are positive constants. When the potentials are constant functions, the author previously proved the existence of positive ground state solutions in the following cases: the noncritical case $\\frac{3+α}{3}<p\\le q<3+α$, the upper half critical case $\\frac{3+α}{3}<p<q=3+α$, and the lower half critical case $\\frac{3+α}{3}=p<q<3+α$, by using the Nehari-Pohozaev manifold method (NoDEA Nonlinear Differential Equations Appl.33(2026)). In the present paper, we extend these results to the case of nonconstant potentials. Under suitable assumptions on $V_1(x)$, $V_2(x)$, and $λ$, we prove the existence of nontrivial ground state solutions. In the noncritical and upper half critical cases, the main tools are Jeanjean's monotonicity trick and a global compactness lemma. For these cases, we establish a refined version of the splitting lemma by relaxing the standard growth assumption at the origin from $o(|t|)$ to the optimal $o(|t|^{α/3})$, thereby significantly broadening the applicable class of nonlinearities. In contrast, for the lower half critical case $p=\\frac{3+α}{3}$, the splitting lemma is no longer valid. To overcome this essential difficulty, we obtain a ground state solution directly as a minimizer on the Nehari-Pohozaev manifold by imposing a slightly stronger condition on the potentials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18405",
  "author_total": 1,
  "authors": [
    {
      "name": "Hiroshi Matsuzawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0q7cnkf9944fm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18405",
  "fulltext_url": null,
  "id": "0q7cnkf9944fm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18405",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213495389",
  "pdf_url": "https://arxiv.org/pdf/2609.18405",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0q7cnkf9944fm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18405",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18405"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Existence of ground state solutions to Kirchhoff--Choquard system in $\\mathbb{R}^3$ with nonconstant potentials",
  "title_text": "Existence of ground state solutions to Kirchhoff--Choquard system in ℝ^3 with nonconstant potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/0q7cnkf9944fm",
  "venue": "arXiv",
  "versions": []
}