{
  "id": "2303.14610",
  "version": "v1",
  "published": "2023-03-26T03:08:59.000Z",
  "updated": "2023-03-26T03:08:59.000Z",
  "title": "Uniqueness and nondegeneracy of ground states for $(-Δ)^su+u=2(I_2\\star u^2)u$ in $\\mathbb{R}^N$ when $s$ is close to 1",
  "authors": [
    "Huxiao Luo"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1301.4868 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we study the uniqueness and nondegeneracy of ground states to a fractional Choquard equation of the form: $(-\\Delta)^su+u=2(I_2\\star u^2)u$ where $s\\in(0,1)$ is sufficiently close to $1$. Our method is to make a continuation argument with respect to the power $s\\in(0,1)$ appearing in $(-\\Delta)^s$. This approach is based on [M. M. Fall and E. Valdinoci, Comm. Math. Phys., 329 (2014) 383-404].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-26T03:08:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A02",
      "35B20",
      "35J61"
    ],
    "keywords": [
      "ground states",
      "uniqueness",
      "nondegeneracy",
      "fractional choquard equation",
      "continuation argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}