{
  "id": "2312.00465",
  "version": "v1",
  "published": "2023-12-01T10:01:15.000Z",
  "updated": "2023-12-01T10:01:15.000Z",
  "title": "Uniqueness and nondegeneracy of ground states for the Schrödinger-Newton equation with power nonlinearity",
  "authors": [
    "Huxiao Luo"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2112.05869 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we study the Schr\\\"{o}dinger-Newton equation \\begin{equation} -\\Delta u+\\lambda u=\\frac{1}{4\\pi}\\left(\\frac{1}{|x|}\\star u^{2}\\right)u+|u|^{q-2}u \\quad \\text{in}~\\mathbb{R}^3, \\end{equation} where $\\lambda\\in\\mathbb{R}_+$, $q\\in (2,3)\\cup(3, 6)$. By investigating limit profiles of ground states as $\\lambda\\to0^+$ or $\\lambda\\to+\\infty$, we prove the uniqueness of ground states. By the action of the linearized eqaution with respect to decomposition into spherical harmonics, we obtain the nondegeneracy of ground states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-01T10:01:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground states",
      "schrödinger-newton equation",
      "power nonlinearity",
      "uniqueness",
      "nondegeneracy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}