{
  "abstract": "Consider \\begin{equation*}\\ \\left\\{ \\begin{aligned} -\\mathcal_{λ,Λ}^{+}(D^{2}u)&=μu+a(x)u^{p}\\quad\\text{in}~Ω,\\\\ u&=0\\quad\\text{on}~~\\partialΩ, \\end{aligned} \\right. \\end{equation*} where $ \\ Omega$ is a smooth bounded domain, $a$ is a continuous function which is allowed to change sign. Moreover, the set of zeros of $a$ may have a non-empty interior. The main objective of this article is to establish a uniform bound on the set of positive solutions of the above problem. This approach requires a suitable Liouville-type theorem. We first prove the Liouville-type theorem for $-\\mathcal_{λ,Λ}^{+}(D^{2}v)=h(x_{1})f(v),$ where \\(h\\) is a strictly increasing one-dimensional weight and \\(f\\) is positive and nondecreasing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13486",
  "author_total": 3,
  "authors": [
    {
      "name": "Karan Rathore"
    },
    {
      "name": "Mohan Mallick"
    },
    {
      "name": "Ram Baran Verma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3xgnmmvbtv976.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13486",
  "fulltext_url": null,
  "id": "3xgnmmvbtv976",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13486",
  "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": "W7221572354",
  "pdf_url": "https://arxiv.org/pdf/2610.13486",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3xgnmmvbtv976.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13486",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13486"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted Liouville Theorems and A Priori Bounds for Indefinite Superlinear Equations with Pucci's Maximal Operator",
  "title_text": "Weighted Liouville Theorems and A Priori Bounds for Indefinite Superlinear Equations with Pucci's Maximal Operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/3xgnmmvbtv976",
  "venue": "arXiv",
  "versions": []
}