{
  "abstract": "We study positive radial singular solutions of $-Δu=f(u)$ in two space dimensions. Fujishima, Ioku, Ruf, and Terraneo constructed such solutions under asymptotic assumptions on $f$ and an additional convergence-rate condition, denoted by $(f_3)$. We prove their local existence result, with the same approximate solution and remainder estimate, under the original assumptions $(f_1)$ and $(f_2)$ alone. The proof combines a contraction on finite intervals with a nonlinear energy estimate uniform in the terminal point and requires only $C^2$ regularity of $f$ near infinity. We also obtain derivative asymptotics and, under additional global assumptions, a singular Dirichlet solution which solves the equation distributionally across the origin. An analytic oscillatory example satisfies our hypotheses but violates both $(f_3)$ and the derivative assumptions of Kikuchi and Kumagai. For every fixed finite iterate of the exponential of order at least two, we verify the hypotheses and quantify the remainder; condition $(f_3)$ fails for all iterates of order at least three.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04520",
  "author_total": 4,
  "authors": [
    {
      "name": "Y. Fujishima"
    },
    {
      "name": "N. Ioku"
    },
    {
      "name": "B. Ruf"
    },
    {
      "name": "E. Terraneo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8kxm2c0rx45dj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04520",
  "fulltext_url": null,
  "id": "8kxm2c0rx45dj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04520",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8kxm2c0rx45dj.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A remark on singular solutions of semilinear elliptic equations in two dimensions",
  "title_text": "A remark on singular solutions of semilinear elliptic equations in two dimensions",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/8kxm2c0rx45dj",
  "venue": "arXiv",
  "versions": []
}