{
  "id": "1711.01438",
  "version": "v1",
  "published": "2017-11-04T13:48:59.000Z",
  "updated": "2017-11-04T13:48:59.000Z",
  "title": "Existence of heteroclinic solution for a double well potential equation in an infinite cylinder of $\\mathbb{R}^N$",
  "authors": [
    "Claudianor O. Alves"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper concernes with the existence of heteroclinic solutions for the following class of elliptic equations $$ -\\Delta{u}+A(\\epsilon x, y)V'(u)=0, \\quad \\mbox{in} \\quad \\Omega, $$ where $\\epsilon >0$, $\\Omega=\\R \\times \\D$ is an infinite cylinder of $\\mathbb{R}^N$ with $N \\geq 2$. Here, we have considered a large class of potential $V$ that includes the Ginzburg-Landau potential $V(t)=(t^{2}-1)^{2}$ and two geometric conditions on the function $A$. In the first condition we assume that $A$ is asymptotic at infinity to a periodic function, while in the second one $A$ satisfies $$ 0<A_0=A(0,y)=\\inf_{(x,y) \\in \\Omega}A(x,y) < \\liminf_{|(x,y)| \\to +\\infty}A(x,y)=A_\\infty<\\infty, \\quad \\forall y \\in \\D. $$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-04T13:48:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite cylinder",
      "heteroclinic solution",
      "potential equation",
      "periodic function",
      "elliptic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}