{
  "abstract": "We study oscillation of the second-order delay equation \\[ x''(t)=x(τ(t)), \\] with a nondecreasing delayed argument $τ(t)\\le t$ satisfying $τ(t)\\overset{t\\to\\infty}{\\to}\\infty$. Set \\begin{equation*} a=\\liminf_{t\\to\\infty}(t-τ(t)),\\qquad b=\\limsup_{t\\to\\infty}(t-τ(t)). \\end{equation*} We describe a continuous strictly decreasing function \\begin{equation} β:[0,2/e]\\longrightarrow[2/e,\\sqrt2],\\qquad β(0)=\\sqrt2,\\qquadβ(2/e)=2/e, \\notag \\end{equation} such that, if the equation has an eventually positive decreasing solution, then \\begin{equation} a\\leq2/e,\\qquad b\\leβ(a). \\notag \\end{equation} The bound $b\\leβ(a)$ is sharp and interpolates between the classical $\\limsup$ threshold and the $\\liminf$ autonomous threshold. A detailed spectral analysis gives a simple interpretation of the result and links it directly to the oscillation theory of first-order delay equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31732",
  "author_total": 1,
  "authors": [
    {
      "name": "John Ioannis Stavroulakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/901qheg3r9ygy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31732",
  "fulltext_url": null,
  "id": "901qheg3r9ygy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31732",
  "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.CA"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2604|Nonlinear Differential Equations Analysis"
    ]
  ],
  "openalex": "W7214772772",
  "pdf_url": "https://arxiv.org/pdf/2609.31732",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/901qheg3r9ygy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.31732",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Oscillation of Second-Order Delay Equations with Positive Feedback",
  "title_text": "Oscillation of Second-Order Delay Equations with Positive Feedback",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/901qheg3r9ygy",
  "venue": "arXiv",
  "versions": []
}