{
  "abstract": "In this article, we study the Fucik spectrum for operators with rapidly increasing weight, which is defined as a set $\\Sigma$ comprising those $(\\alpha, \\beta) \\in \\mathbb{R}^2$ such that $$\\displaylines{ L u:=-\\Delta u-\\frac{1}{2}(x \\cdot \\nabla u)=\\alpha u^{+}-\\beta u^{-}, \\quad\\text{in } \\mathbb{R}^N,\\cr u\\in X, }$$ has a non-trivial solution $u$, where, $N\\geq1$, $u^{ \\pm}=\\max ( \\pm u, 0)$, $u=u^{+}-u^{-}$. The existence of a first nontrivial curve $\\mathcal{C}$ of this spectrum, along with some of its properties (e.g., Lipschitz continuity, strict decrease and asymptotic behavior) is investigated in this paper. Our difficulty is that the problem is defined on the whole space $\\mathbb{R}^N$, and therefore certain estimates do not carry over from the Fucik problem on bounded domains. As an application, we establish the multiplicity of solutions to the problem $$\\displaylines{ -\\Delta u-\\frac{1}{2}(x \\cdot \\nabla u)=f(x,u), \\quad\\text{in } \\mathbb{R}^N,\\cr u\\in X, }$$ where, $N\\geq1$ and the nonlinearity $f$ is asymptotically linear at zero and at infinity.",
  "abstract_shown": true,
  "affiliations": [
    "Beijing Technology and Business Univ., Beijing, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jinzi Bai"
    },
    {
      "affs": [
        0
      ],
      "name": "Fei Fang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0y5y85t8v4k4n.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": "http://ejde.math.txstate.edu/Volumes/2026/58/abstr.html",
  "id": "0y5y85t8v4k4n",
  "issns": [
    "1072-6691"
  ],
  "landing_url": "http://ejde.math.txstate.edu/Volumes/2026/58/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": "2026-07-01",
  "publisher": "Texas State University",
  "ris": "https://research.draconitic.com/paper/0y5y85t8v4k4n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:04Z",
      "native_id": "2b3a7ea4044146a2bf67f8662ff45ceb",
      "source": "doaj",
      "url": "http://ejde.math.txstate.edu/Volumes/2026/58/abstr.html"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "lcc:QA1-939",
      "subfield": "general"
    }
  ],
  "title": "Fucik spectrum for operators with rapidly increasing weight and applications",
  "title_text": "Fucik spectrum for operators with rapidly increasing weight and applications",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:04Z",
  "url": "https://research.draconitic.com/paper/0y5y85t8v4k4n",
  "venue": "Electronic Journal of Differential Equations",
  "versions": []
}