{
  "id": "1803.07579",
  "version": "v1",
  "published": "2018-03-20T18:09:32.000Z",
  "updated": "2018-03-20T18:09:32.000Z",
  "title": "Schrödinger-Maxwell systems on compact Riemannian manifolds",
  "authors": [
    "Csaba Farkas"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we are focusing to the following Schr\\\"odinger-Maxwell system $(\\mathcal{SM}_{\\Psi(\\lambda,\\cdot)}^{e})$: \\[ \\begin{cases} -\\Delta_{g}u+\\beta(x)u+eu\\phi=\\Psi(\\lambda,x)f(u) & \\mathrm{in}\\ M -\\Delta_{g}\\phi+\\phi=qu^{2} & \\mathrm{\\mathrm{in}\\ M} \\end{cases} \\] where $(M,g)$ is a 3-dimensional compact Riemannian manifold without boundary, $e,q>0$ are positive numbers, $f:\\mathbb{R}\\to\\mathbb{R}$ is a continuous function, $\\beta\\in C^{\\infty}(M)$ and $\\Psi\\in C^{\\infty}(\\mathbb{R}_{+}\\times M)$ are positive functions. By various variational approaches, existence of multiple solutions of the problem $(\\mathcal{SM}_{\\Psi(\\lambda,\\cdot)}^{e})$ is established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-20T18:09:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact riemannian manifold",
      "schrödinger-maxwell systems",
      "variational approaches",
      "multiple solutions",
      "continuous function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}