{
  "abstract": "In this paper, we develop a method of invariant sets of descending flows to demonstrate the existence of a sign-changing solution for a class of elliptic problems involving mixed local and nonlocal operators with zero Dirichlet boundary conditions. In particular, we prove the existence of infinitely many sign-changing solutions. Next, we employ the Nehari manifold techniques with a constrained variational approach and Brouwer degree theory to establish the existence of a least-energy sign-changing solution and a ground state solution. Moreover, we prove that the energy for the least-energy sign-changing solution is strictly greater than twice the ground-state energy. The results obtained in this paper are completely new in the context of mixed local and nonlocal operators, even for the linear case $ p = 2 $. Specifically, this work extends the celebrated results of Bartsch et al. [Proc. Lond. Math. Soc. (3), 91(1): 129–152, 2005] and Chang et al. [Adv. Nonlinear Stud., 19(1): 29–53, 2019] to the mixed local and nonlocal $ p $-Laplace operator.",
  "abstract_shown": true,
  "affiliations": [
    "National Institute of Technology Calicut , Kozhikode , 673601 , India",
    "National Institute of Technology Calicut, Kozhikode, 673601, India"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Souvik Bhowmick"
    },
    {
      "affs": [
        1
      ],
      "name": "Sekhar Ghosh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87gph74rhznqr.bib",
  "cited_by": 5,
  "doi": "10.3934/dcdss.2026184",
  "fulltext_url": null,
  "id": "87gph74rhznqr",
  "issns": [
    "1937-1179",
    "1937-1632"
  ],
  "landing_url": "https://doi.org/10.3934/dcdss.2026184",
  "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": [
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7168359860",
  "pdf_url": "https://www.aimsciences.org/data/article/export-pdf?id=6a57488cbabc735ed83f34d9",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-15",
  "publisher": "American Institute of Mathematical Sciences",
  "ris": "https://research.draconitic.com/paper/87gph74rhznqr.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:00Z",
      "native_id": "W7168359860",
      "source": "openalex",
      "url": "https://doi.org/10.3934/dcdss.2026184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Nonlinear Partial Differential Equations",
      "subfield": "general"
    }
  ],
  "title": "On sign-changing solutions for mixed local and nonlocal $ p $ -Laplace operator",
  "title_text": "On sign-changing solutions for mixed local and nonlocal $ p $ -Laplace operator",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T13:20:22Z",
  "url": "https://research.draconitic.com/paper/87gph74rhznqr",
  "venue": "Discrete and Continuous Dynamical Systems - S",
  "versions": []
}