{
  "id": "1504.03008",
  "version": "v1",
  "published": "2015-04-12T19:12:08.000Z",
  "updated": "2015-04-12T19:12:08.000Z",
  "title": "On the periodic solutions of discontinuous piecewise differential systems",
  "authors": [
    "Jaume Llibre",
    "Douglas Duarte Novaes"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Motivated by problems coming from different areas of the applied science we study the periodic solutions of the following differential system $$x'(t)=F_0(t,x)+\\varepsilon F_1(t,x)+\\varepsilon^2 R(t,x,\\varepsilon),$$ when $F_0$, $F_1$, and $R$ are discontinuous piecewise functions, and $\\varepsilon$ is a small parameter. It is assumed that the manifold $\\mathbb{Z}$ of all periodic solutions of the unperturbed system $x'=F_0(t,x)$ has dimension $n$ or smaller then $n$. The averaging theory is one of the best tools to attack this problem. This theory is completely developed when $F_0$, $F_1$ and $R$ are continuous functions, and also when $F_0=0$ for a class of discontinuous differential systems. Nevertheless does not exist the averaging theory for studying the periodic solutions of discontinuous differential system when $F_0\\neq0$. In this paper we develop this theory for a big class of discontinuous differential systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-12T19:12:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G15",
      "34C29",
      "37C30"
    ],
    "keywords": [
      "periodic solutions",
      "discontinuous piecewise differential systems",
      "discontinuous differential system",
      "averaging theory",
      "best tools"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150403008L"
    }
  }
}