{
  "abstract": "Let $Ω\\subset\\R^N$, $N\\ge2$, be a bounded domain and let $1<p<\\infty$. Inspired by the exponential case treated in \\cite{BO2026}, we study the quasilinear Schrödinger--Maxwell system \\[ \\begin{cases} -Δ_p u+ψG'(u)=f &\\text{in }Ω,\\\\ -Δ_pψ=G(u) &\\text{in }Ω,\\\\ u=ψ=0 &\\text{on }\\partialΩ, \\end{cases} \\] where $G\\in C^1(\\R)$ is even, convex, nonnegative and nontrivial, with $G(0)=0$, and satisfies \\[ G(t)\\lesssim 1+|G'(t)| \\qquad\\text{for large }|t|. \\] Under the assumption \\[ |f|\\ln(1+|f|)\\in L^1(Ω), \\] we prove the existence of a finite-energy weak solution and show that the solution is a saddle point of the associated functional.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10878",
  "author_total": 1,
  "authors": [
    {
      "name": "Genival da Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bds2y0v54fqts.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10878",
  "fulltext_url": null,
  "id": "bds2y0v54fqts",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10878",
  "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": "W7212316379",
  "pdf_url": "https://arxiv.org/pdf/2609.10878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bds2y0v54fqts.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A $p$-Laplacian Schrödinger--Maxwell system with rapidly growing nonlinearities",
  "title_text": "A p-Laplacian Schrödinger--Maxwell system with rapidly growing nonlinearities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/bds2y0v54fqts",
  "venue": "arXiv",
  "versions": []
}