{
  "id": "2010.12538",
  "version": "v1",
  "published": "2020-10-19T09:29:55.000Z",
  "updated": "2020-10-19T09:29:55.000Z",
  "title": "Existence of infinitely many solutions for a class of fractional Schrödinger equations in $\\mathbb{R}^N$ with combined nonlinearities",
  "authors": [
    "Sofiane Khoutir"
  ],
  "comment": "15 pages, research paper",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is devoted to the following class of nonlinear fractional Schr\\\"odinger equations: \\begin{equation*} (-\\Delta)^{s} u + V(x)u = f(x,u) + \\lambda g(x,u), \\quad \\text{in}\\: \\mathbb{R}^N, \\end{equation*} where $s\\in (0,1)$, $N>2s$, $(-\\Delta)^{s}$ stands for the fractional Laplacian, $\\lambda\\in \\mathbb{R}$ is a parameter, $V\\in C(\\mathbb{R}^N,R)$, $f(x,u)$ is superlinear and $g(x,u)$ is sublinear with respect to $u$, respectively. We prove the existence of infinitely many high energy solutions of the aforementioned equation by means of the Fountain theorem. Some recent results are extended and sharply improved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-19T09:29:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35J20",
      "35J60"
    ],
    "keywords": [
      "fractional schrödinger equations",
      "nonlinearities",
      "high energy solutions",
      "fractional laplacian",
      "fountain theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}