{
  "id": "2406.01772",
  "version": "v1",
  "published": "2024-06-03T20:25:57.000Z",
  "updated": "2024-06-03T20:25:57.000Z",
  "title": "Homoclinic Solution to Zero of a Non-autonomous, Nonlinear, Second Order Differential Equation with Quadratic Growth on the Derivative",
  "authors": [
    "Pablo dos Santos Corrêa Junior",
    "Luiz Fernando de Oliveira Faria"
  ],
  "categories": [
    "math.CA",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "This work aims to obtain a positive, smooth, even, and homoclinic to zero (i.e zero at infinity) solution to a non-autonomous, second-order, nonlinear differential equation involving quadratic growth on the derivative. We apply Galerkin's method combined with Strauss' approximation on the term involving the first derivative to obtain weak solutions. We also study the regularity of the solutions and the dependence on their existence with a parameter",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-03T20:25:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A34",
      "34C37",
      "34D10",
      "34K12",
      "34L30"
    ],
    "keywords": [
      "second order differential equation",
      "quadratic growth",
      "homoclinic solution",
      "derivative",
      "non-autonomous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}