{
  "id": "1307.6895",
  "version": "v1",
  "published": "2013-07-25T23:41:18.000Z",
  "updated": "2013-07-25T23:41:18.000Z",
  "title": "On the Schrödinger equation with singular potentials",
  "authors": [
    "Jaime Angulo Pava",
    "Lucas C. F. Ferreira"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the Cauchy problem for the non-linear Schr\\\"odinger equation with singular potentials. For point-mass potential and nonperiodic case, we prove existence and asymptotic stability of global solutions in weak-L^{p} spaces. Specific interest is give to the point-like $\\delta$ and $\\delta'$ impurity and for two $\\delta$-interactions in one dimension. We also consider the periodic case which is analyzed in a functional space based on Fourier transform and local-in-time well-posedness is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-25T23:41:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A05",
      "35A07",
      "35C15",
      "35B40",
      "35B10"
    ],
    "keywords": [
      "singular potentials",
      "schrödinger equation",
      "local-in-time well-posedness",
      "nonperiodic case",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.6895A"
    }
  }
}