{
  "abstract": "We study a nonlinear Poisson-Poisson system in a bounded domain $\\Omega\\subset\\mathbb{R}^N$, $N\\geq 3$, whose reduced form is the nonlocal elliptic equation $-\\Delta u+\\lambda(-\\Delta)^{-1}u=|u|^{p-2}u$. We assume that $\\lambda\\in(-\\lambda_1(\\Omega)^2,\\infty)$, where $\\lambda_1(\\Omega)$ denotes the first Dirichlet eigenvalue of $-\\Delta$ in $\\Omega$, and that the exponent is subcritical, $2<p<2^*=2N/(N-2)$. We first show that, throughout this coercive range, the quadratic part of the associated energy functional defines a norm equivalent to the standard norm of $H_0^1(\\Omega)$. We then establish the Palais-Smale condition on the Nehari manifold and use the Krasnosel'skii genus to prove the existence of infinitely many pairs of nontrivial weak solutions. More precisely, there exists a sequence of solutions $(u_k,\\phi_{u_k})$ such that $\\|u_k\\|_\\lambda^2\\to\\infty$. A three-dimensional finite element experiment illustrates two distinct discrete solutions, one of which changes sign.",
  "abstract_shown": true,
  "affiliations": [
    "Univ. Nacional Jorge Basadre Grohmann, Tacna, Peru",
    "Univ. de Concepcion, Chile",
    "Univ. de Tarapaca, Arica, Chile"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Raul Nina-Mollisaca"
    },
    {
      "affs": [
        0
      ],
      "name": "Julio Huayta-Centeno"
    },
    {
      "affs": [
        1
      ],
      "name": "Mauricio Sepulveda-Cortes"
    },
    {
      "affs": [
        2
      ],
      "name": "Octavio Vera-Villagran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dy9j2kx79v9xx.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": "http://ejde.math.txstate.edu/Volumes/2026/83/abstr.html",
  "id": "dy9j2kx79v9xx",
  "issns": [
    "1072-6691"
  ],
  "landing_url": "http://ejde.math.txstate.edu/Volumes/2026/83/abstr.html",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ]
  ],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "Texas State University",
  "ris": "https://research.draconitic.com/paper/dy9j2kx79v9xx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:09Z",
      "native_id": "a5e657b853514481941b58c30e9f02ed",
      "source": "doaj",
      "url": "http://ejde.math.txstate.edu/Volumes/2026/83/abstr.html"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "lcc:QA1-939",
      "subfield": "general"
    }
  ],
  "title": "Existence of infinitely many solutions for nonlinear Poisson-Poisson elliptic systems",
  "title_text": "Existence of infinitely many solutions for nonlinear Poisson-Poisson elliptic systems",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:09Z",
  "url": "https://research.draconitic.com/paper/dy9j2kx79v9xx",
  "venue": "Electronic Journal of Differential Equations",
  "versions": []
}