{
  "id": "1606.02800",
  "version": "v1",
  "published": "2016-06-09T02:03:13.000Z",
  "updated": "2016-06-09T02:03:13.000Z",
  "title": "Boundedness and persistence of delay differential equations with mixed nonlinearity",
  "authors": [
    "Leonid Berezansky",
    "Elena Braverman"
  ],
  "comment": "24 pages, published in Applied Mathematics and Computation, 2016",
  "journal": "Applied Mathematics and Computation 279 (2016) 154-169",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a nonlinear equation with several variable delays $$ \\dot{x}(t)=\\sum_{k=1}^m f_k(t, x(h_1(t)),\\dots,x(h_l(t)))-g(t,x(t)), $$ where the functions $f_k$ increase in some variables and decrease in the others, we obtain conditions when a positive solution exists on $[0, \\infty)$, as well as explore boundedness and persistence of solutions. Finally, we present sufficient conditions when a solution is unbounded. Examples include the Mackey-Glass equation with non-monotone feedback and two variable delays; its solutions can be neither persistent nor bounded, unlike the well studied case when these two delays coincide.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-09T02:03:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34K25",
      "34K60",
      "92D25",
      "34K23"
    ],
    "keywords": [
      "delay differential equations",
      "mixed nonlinearity",
      "boundedness",
      "persistence",
      "variable delays"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}