{
  "id": "1904.12888",
  "version": "v1",
  "published": "2019-04-29T18:10:14.000Z",
  "updated": "2019-04-29T18:10:14.000Z",
  "title": "On stability of linear neutral differential equations with variable delays",
  "authors": [
    "Leonid Berezansky",
    "Elena Braverman"
  ],
  "comment": "28 pages. to appear in Czechoslovak Mathematical Journal, published online",
  "doi": "10.21136/CMJ.2019.0534-17",
  "categories": [
    "math.DS"
  ],
  "abstract": "We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays $$ \\dot{x}(t)-a(t)\\dot{x}(g(t))+b(t)x(h(t))=0, $$ where $$ |a(t)|<1,~ b(t)\\geq 0, ~h(t)\\leq t, ~g(t)\\leq t, $$ and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-29T18:10:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K40",
      "34K20",
      "34K06",
      "45J05"
    ],
    "keywords": [
      "linear neutral differential equations",
      "variable delays",
      "explicit exponential stability conditions",
      "linear scalar neutral equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}