{
  "abstract": "We study a class of nonlinear nonlocal elliptic equations in $\\mathbb{R}^N$ involving superpositions of Hartree-type nonlinearities. Motivated by the Schrödinger-Poisson-Slater system, these equations arise as natural generalizations of problems with a single nonlocal interaction term. More precisely, we consider equations driven by a family of Riesz potentials weighted by a positive Borel measure, which gives rise to a superposed nonlocal operator. To treat this problem variationally, we introduce suitable functional settings, namely the superposed Coulomb space and the associated superposed Coulomb-Sobolev space, and study their main properties. Combining variational methods with a recently developed scaling-based critical point theory, we prove existence and multiplicity results for radial solutions. We also investigate a Brezis-Nirenberg-type problem and obtain multiplicity results near eigenvalues of an associated nonlinear eigenvalue problem. Our results extend previous works on single Hartree-type equations and provide a unified framework for treating superpositions of nonlocal interactions of Hartree type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.05592",
  "author_total": 2,
  "authors": [
    {
      "name": "Artur Jorge Marinho"
    },
    {
      "name": "Kanishka Perera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c60qp4khrmsyv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.05592",
  "fulltext_url": null,
  "id": "c60qp4khrmsyv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.05592",
  "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": "W7163637711",
  "pdf_url": "https://arxiv.org/pdf/2606.05592",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c60qp4khrmsyv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2606.05592",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.05592"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Solutions to critical equations with a superposition of nonlocal Hartree-type nonlinearities",
  "title_text": "Solutions to critical equations with a superposition of nonlocal Hartree-type nonlinearities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/c60qp4khrmsyv",
  "venue": "arXiv",
  "versions": []
}