{
  "abstract": "We consider the critical Hénon equation $-Δu=|x|^αu^{(N+2+2α)/(N-2)}$ in $\\mathbb{R}^N$, $N\\ge3$. Gladiali, Grossi, and Neves (\\emph{Advances in Mathematics}, 2013) constructed nonradial continua bifurcating at $α_k=2(k-1)$, $k\\ge2$, and conjectured that these continua are confined to the even parameters. Jiang and Xiong (2026) disproved this conjecture by obtaining nonradial solutions in punctured neighborhoods of $α_k$ for even $k>(N-2)/2$. We prove that positive nonradial finite-energy entire solutions exist for every $α>2$ in every dimension $N\\ge3$. The proof introduces a global variational construction by direct minimization on a monotonicity cone on the Emden--Fowler cylinder. Angular and axial order restore compactness in every finite $L^r$, $r>2$, despite Sobolev supercriticality, and invariance of the linear resolvent yields the full equation. This constructs a solution at each prescribed parameter without continuing local bifurcation branches. The solutions have Newtonian decay, are invariant under $O(N-1)\\times O(1)$ and the Kelvin transform, and have energy strictly below the radial level. We also obtain a second solution for every $α>6$ in even dimensions, nonvertical branches at every $α_k$ with $k\\ge2$ even without dimension restrictions, a cubic energy law, and rigidity near $α=0$ under bounded cylindrical amplitude.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02420",
  "author_total": 1,
  "authors": [
    {
      "name": "Phuong Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pvw5z8hjbksd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02420",
  "fulltext_url": null,
  "id": "8pvw5z8hjbksd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02420",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02420",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pvw5z8hjbksd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02420",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02420"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nonradial entire solutions of the critical Hénon equation for every $α>2$",
  "title_text": "Nonradial entire solutions of the critical Hénon equation for every α>2",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8pvw5z8hjbksd",
  "venue": "arXiv",
  "versions": []
}