{
  "id": "2411.06149",
  "version": "v1",
  "published": "2024-11-09T11:29:21.000Z",
  "updated": "2024-11-09T11:29:21.000Z",
  "title": "An elementary proof of the existence and uniqueness of solutions to an initial value problem",
  "authors": [
    "Luca Tanganelli Castrillón"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this note, we show a classical result on the local existence and uniqueness of a solution to an initial value problem subject to a Lipschitz condition. We use only elementary tools from mathematical analysis, without involving any integration. We proceed by showing that the Cauchy iterates converge on a dense subset of the interval and subsequently proving that the extension of this limit function to the whole interval is a solution to the Cauchy problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-09T11:29:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A12"
    ],
    "keywords": [
      "elementary proof",
      "uniqueness",
      "initial value problem subject",
      "cauchy iterates converge",
      "local existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}