{
  "abstract": "We establish a new abstract minimax theorem for obtaining ground-state critical points of a class of \\(C^{1}\\)-functionals. The central feature of this class is that the associated Nehari set is not necessarily a differentiable manifold, but is homeomorphic to a (possibly non-complete) submanifold of the unit sphere. This occurs for functionals whose fibering maps \\(t \\mapsto I(tu)\\) possess a unique global maximum point only when \\(u\\) belongs to an open cone in the underlying Banach space. A lower semicontinuous boundary barrier, which may be finite, controls minimizing sequences near the boundary of the spherical cone. As a consequence, we provide a general minimax characterization of the ground-state energy level. Elliptic applications complement existing results and include superlinear and quasilinear problems with finite barriers, including thresholds depending on the profile of a first eigenfunction and its gradient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31262",
  "author_total": 3,
  "authors": [
    {
      "name": "Denilson S. Pereira"
    },
    {
      "name": "João R. Santos Júnior"
    },
    {
      "name": "João F. F. Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eawthbh4zxsk8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31262",
  "fulltext_url": null,
  "id": "eawthbh4zxsk8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31262",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.31262",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eawthbh4zxsk8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31262",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31262"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A New Minimax Theorem for a Class of $C^1$-Functionals",
  "title_text": "A New Minimax Theorem for a Class of C^1-Functionals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/eawthbh4zxsk8",
  "venue": "arXiv",
  "versions": []
}