{
  "id": "2012.10726",
  "version": "v1",
  "published": "2020-12-19T16:11:16.000Z",
  "updated": "2020-12-19T16:11:16.000Z",
  "title": "Stability and oscillation of linear delay differential equations",
  "authors": [
    "John Ioannis Stavroulakis",
    "Elena Braverman"
  ],
  "comment": "22 pages, one figure, submitted to Journal of Differential Equations on June 20, 2019",
  "categories": [
    "math.DS"
  ],
  "abstract": "There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\\prime}(t)+c(t)x(\\tau(t))=0,~~t\\geq 0, $$ where $c$ is locally integrable of any sign, $\\tau(t)\\leq t$ is Lebesgue measurable, $\\lim_{t\\rightarrow\\infty}\\tau(t)=\\infty$, we obtain sharp results, relating the speed of oscillation and stability. We thus unify the classical results of Myshkis and Lillo. We also generalise the $3/2-$stability criterion to the case of measurable parameters, improving $1+1/e$ to the sharp $3/2$ constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-19T16:11:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K20",
      "34K25"
    ],
    "keywords": [
      "linear delay differential equations",
      "oscillation",
      "close connection",
      "stability criterion",
      "sharp results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}