{
  "id": "2401.11111",
  "version": "v1",
  "published": "2024-01-20T04:17:24.000Z",
  "updated": "2024-01-20T04:17:24.000Z",
  "title": "New type of solutions for Schrödinger equations with critical growth",
  "authors": [
    "Yuan Gao",
    "Yuxia Guo"
  ],
  "comment": "38 pages, 0 figures",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We consider the following nonlinear Schr\\\"odinger equations with critical growth: \\begin{equation} - \\Delta u + V(|y|)u=u^{\\frac{N+2}{N-2}},\\quad u>0 \\ \\ \\mbox{in} \\ \\mathbb {R}^N, \\end{equation} where $V(|y|)$ is a bounded positive radial function in $C^1$, $N\\ge 5$. By using a finite reduction argument, we show that if $r^2V(r)$ has either an isolated local maximum or an isolated minimum at $r_0>0$ with $V(r_0)>0$, there exists infinitely many non-radial large energy solutions which are invariant under some sub-groups of $O(3)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-20T04:17:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35B33",
      "35B38"
    ],
    "keywords": [
      "critical growth",
      "schrödinger equations",
      "non-radial large energy solutions",
      "finite reduction argument",
      "bounded positive radial function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}