{
  "id": "2205.10452",
  "version": "v1",
  "published": "2022-05-20T22:26:39.000Z",
  "updated": "2022-05-20T22:26:39.000Z",
  "title": "Existence and limit behavior of least energy solutions to constrained Schrödinger-Bopp-Podolsky systems in $\\mathbb{R}^3$",
  "authors": [
    "Gustavo de Paula Ramos",
    "Gaetano Siciliano"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Consider the following Schr\\\"odinger-Bopp-Podolsky system in $\\mathbb{R}^3$ under an $L^2$-norm constraint, \\[ \\begin{cases} -\\Delta u + \\omega u + \\phi u = u|u|^{p-2},\\newline -\\Delta \\phi + a^2\\Delta^2\\phi=4\\pi u^2,\\newline \\|u\\|_{L^2}=\\rho, \\end{cases} \\] where $a,\\rho>0$ and our unknowns are $u,\\phi\\colon\\mathbb{R}^3\\to\\mathbb{R}^3$ and $\\omega\\in\\mathbb{R}$. We prove that if $2<p<3$ (resp., $3<p<10/3$) and $\\rho>0$ is sufficiently small (resp., sufficiently large), then this system admits a least energy solution. Moreover, we prove that if $2<p<14/5$ and $\\rho>0$ is sufficiently small, then least energy solutions are radially symmetric up to translation and as $a\\to 0$, they converge to a least energy solution of the Schr\\\"odinger-Poisson-Slater system under the same $L^2$-norm constraint.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-20T22:26:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B38"
    ],
    "keywords": [
      "energy solution",
      "constrained schrödinger-bopp-podolsky systems",
      "limit behavior",
      "norm constraint",
      "sufficiently small"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}