{
  "abstract": "In this article, we study the semi-linear elliptic problem: \\begin{equation*} -Δ_{\\mathbb{B}^N} u \\, - \\, λu = |u|^{p-1}u, \\quad u \\in H^{1}(\\mathbb{B}^N), \\end{equation*} where $N \\geq 3$, $λ> \\frac{N(N-2)}{4}$, and $1 < p \\leq 2^*-1$. Here, $\\mathbb{B}^N$ represents the Poincaré ball model of the hyperbolic space, and $H^{1}(\\mathbb{B}^N)$ denotes the Sobolev space on $\\mathbb{B}^N$. In the critical case $p = 2^*-1$, with $λ< \\frac{(N-1)^2}{4}$ and $N \\geq 4$, we establish the existence and multiplicity of nonradial sign-changing solutions. Moreover, our result answers an open question: ``the existence of sign-changing solutions in the lower dimensions $4 \\leq N \\leq 6$\". We also prove a partial non-existence result for a large class of symmetric solutions when $λ> \\frac{(N-1)^2}{4}$, based on a quantitative orbit packing condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.25683",
  "author_total": 2,
  "authors": [
    {
      "name": "Atanu Manna"
    },
    {
      "name": "Bhakti Bhusan Manna"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01q4yhq597ara.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.25683",
  "fulltext_url": null,
  "id": "01q4yhq597ara",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.25683",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7165881725",
  "pdf_url": "https://arxiv.org/pdf/2606.25683",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01q4yhq597ara.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.25683",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.25683"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Existence and non-existence of nonradial solutions to an elliptic equation on hyperbolic space with critical and subcritical nonlinearities",
  "title_text": "Existence and non-existence of nonradial solutions to an elliptic equation on hyperbolic space with critical and subcritical nonlinearities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/01q4yhq597ara",
  "venue": "arXiv",
  "versions": []
}