{
  "id": "1902.08252",
  "version": "v1",
  "published": "2019-02-21T20:33:30.000Z",
  "updated": "2019-02-21T20:33:30.000Z",
  "title": "On stability of linear neutral differential equations in the Hale form",
  "authors": [
    "Leonid Berezansky",
    "Elena Braverman"
  ],
  "comment": "14 pages",
  "journal": "Appl. Math. Comput. 340 (2019), 63-71",
  "doi": "10.1016/j.amc.2018.08.010",
  "categories": [
    "math.DS"
  ],
  "abstract": "We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays $$ (x(t)-a(t)x(g(t)))'=-b(t)x(h(t)), $$ where $|a(t)|<1$, $b(t)\\geq 0$, $h(t)\\leq t$, $g(t)\\leq t$, in the case when the delays $t-h(t)$, $t-g(t)$ are bounded, as well as an asymptotic stability condition, if the delays can be unbounded.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-21T20:33:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K40",
      "34K20",
      "34K06",
      "45J05"
    ],
    "keywords": [
      "linear neutral differential equations",
      "hale form",
      "explicit exponential stability conditions",
      "linear scalar neutral equation",
      "asymptotic stability condition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}