{
  "id": "2210.08950",
  "version": "v1",
  "published": "2022-10-17T11:32:30.000Z",
  "updated": "2022-10-17T11:32:30.000Z",
  "title": "Locating and Invariance Theorems of Differential Inclusions Governed by Maximally Monotone Operators",
  "authors": [
    "Minh N. Dao",
    "Hassan Saoud",
    "Michel Théra"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we are interested in studying the asymptotic behavior of the solutions of differential inclusions governed by maximally monotone operators. In the case where the LaSalle's invariance principle is inconclusive, we provide a refined version of the invariance principle theorem. This result derives from the problem of locating the $\\omega$-limit set of a bounded solution of the dynamic. In addition, we propose an extension of LaSalle's invariance principle, which allows us to give a sharper location of the $\\omega$-limit set. The provided results are given in terms of nonsmooth Lyapunov pair-type functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-17T11:32:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximally monotone operators",
      "differential inclusions",
      "invariance theorems",
      "lasalles invariance principle",
      "nonsmooth lyapunov pair-type functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}