{
  "abstract": "We prove a nonexistence theorem for positive potential systems with continuous coefficients satisfying distributional Euler lower bounds and a uniform Dini modulus on normalized logarithmic dilations. The nonlinearities have positive lower logarithmic derivatives and positive primitive-to-endpoint ratios. The common radial kernel is comparable with a Riesz kernel. A localized transport identity, a primitive pressure estimate and implicit amplitude normalization give uniform local energy bounds and a dilation contradiction. And we treats the genuine Green kernel of $-Δ+V$ for nonnegative potentials under annular and Newton composition budgets and a strict gap corrected by the relative Green dilation defect. Relative endpoint differences and an exact virtual-energy cancellation retain local nonlinear energy as the only initial energy hypothesis. Independent representation arguments give these consequences, including even integer orders without initial tails. A compact family of normalized responses also yields universal interior bounds without regular variation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26656",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongtao Hu"
    },
    {
      "name": "Zhouyu Long"
    },
    {
      "name": "Wenming Zou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzrbzsyfk39yv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26656",
  "fulltext_url": null,
  "id": "bzrbzsyfk39yv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26656",
  "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": "W7222997632",
  "pdf_url": "https://arxiv.org/pdf/2610.26656",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzrbzsyfk39yv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26656",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26656"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Weighted potential and Green systems with Dini coefficients and primitive growth",
  "title_text": "Weighted potential and Green systems with Dini coefficients and primitive growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/bzrbzsyfk39yv",
  "venue": "arXiv",
  "versions": []
}