{
  "id": "2108.01421",
  "version": "v1",
  "published": "2021-08-03T11:38:34.000Z",
  "updated": "2021-08-03T11:38:34.000Z",
  "title": "Asymptotic profiles for a nonlinear Schrödinger equation with critical combined powers nonlinearity",
  "authors": [
    "Shiwang Ma",
    "Vitaly Moroz"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study asymptotic behaviour of positive ground state solutions of the nonlinear Schr\\\"odinger equation $$ -\\Delta u+ u=u^{2^*-1}+\\lambda u^{q-1} \\quad {\\rm in} \\ \\ \\mathbb{R}^N, $$ where $N\\ge 3$ is an integer, $2^*=\\frac{2N}{N-2}$ is the Sobolev critical exponent, $2<q<2^*$ and $\\lambda>0$ is a parameter. It is known that as $\\lambda\\to 0$, after a rescaling the ground state solutions of the equation converge to a particular solution of the critical Emden-Fowler equation $-\\Delta u=u^{2^*-1}$. We establish a sharp asymptotic characterisation of such a rescaling, which depends in a non-trivial way on the space dimension $N=3$, $N=4$ or $N\\ge 5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-03T11:38:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35B25",
      "35B40"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "powers nonlinearity",
      "asymptotic profiles",
      "positive ground state solutions",
      "study asymptotic behaviour"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}