{
  "abstract": "We study the inhomogeneous logarithmic Schrödinger equation \\[ i\\partial_tu+Δu+|x|^{-1}u\\log|u|^2=0, \\qquad (t,x)\\in\\R\\times\\R^N,\\quad N\\ge2. \\] For every initial datum in $H^1(\\R^N)$, we establish global existence of weak solutions. We also construct explicit positive stationary solutions and solve the associated Nehari minimization problem. For $ω\\ge0$, the minimizer is unique up to {a constant} phase and is given by \\[ e^{\\frac{N-1}{2}(1+\\sqrt{1+ω})} e^{-(1+\\sqrt{1+ω})|x|}, \\] whereas for $ω<0$ the infimum is zero and is not attained. Finally, we prove that the standing waves associated with these profiles are orbitally stable for $ω>0$ by a variational argument, and orbitally unstable for $-1<ω<-1+(N-1)^{-2}$ by combining spectral analysis, localized energy and mass estimates, and phase modulation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07167",
  "author_total": 1,
  "authors": [
    {
      "name": "Alex H. Ardila"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfgyxf8x0zv5j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07167",
  "fulltext_url": null,
  "id": "dfgyxf8x0zv5j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07167",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07167",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfgyxf8x0zv5j.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07167",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07167"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Orbital stability and instability of standing waves for an inhomogeneous logarithmic Schrödinger equation",
  "title_text": "Orbital stability and instability of standing waves for an inhomogeneous logarithmic Schrödinger equation",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/dfgyxf8x0zv5j",
  "venue": "arXiv",
  "versions": []
}