{
  "abstract": "Given $ρ>0$, we consider the problem \\[ \\text{find $(λ,u) \\in \\mathbb{R} \\times H_0^1(B)$ such that } \\begin{cases} -Δu+λu = |u|^{p-1}u & \\text{in } B \\\\ \\int_B u^2\\,dx = ρ, \\end{cases} \\] where $B$ is a ball in $\\mathbb{R}^N$, $N \\ge 1$, and $1<p<2^*-1$. Without any further restriction on $N$, $ρ$ and $p$, we prove the existence of infinitely many radial solutions, and, in dimension $N \\ge 4$, of at least one non-radial solution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15141",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicola Soave"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7bgxm24j79k6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15141",
  "fulltext_url": null,
  "id": "a7bgxm24j79k6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15141",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213257667",
  "pdf_url": "https://arxiv.org/pdf/2609.15141",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7bgxm24j79k6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15141",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15141"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Normalized solutions to the NLS equation in the ball for any prescribed mass",
  "title_text": "Normalized solutions to the NLS equation in the ball for any prescribed mass",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/a7bgxm24j79k6",
  "venue": "arXiv",
  "versions": []
}