{
  "id": "1811.07191",
  "version": "v2",
  "published": "2018-11-17T17:14:43.000Z",
  "updated": "2018-12-10T20:16:02.000Z",
  "title": "Classification of nonnegative solutions to static Schrödinger-Hartree and Schrödinger-Maxwell equations with combined nonlinearities",
  "authors": [
    "Wei Dai",
    "Zhao Liu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we are concerned with static Schr\\\"{o}dinger-Hartree and Schr\\\"{o}dinger-Maxwell equations with combined nonlinearities. We derive the explicit forms for positive solution $u$ in the critical case and non-existence of nontrivial nonnegative solutions in the subcritical cases (see Theorem \\ref{Thm0} and \\ref{Thm1}). The arguments used in our proof is a variant (for nonlocal nonlinearity) of the direct moving spheres method for fractional Laplacians in \\cite{CLZ}. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., \\emph{Narrow region principle} (Theorem \\ref{Thm2} and \\ref{Thm3}).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-12-10T20:16:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35B06",
      "35B53"
    ],
    "keywords": [
      "schrödinger-maxwell equations",
      "static schrödinger-hartree",
      "classification",
      "nonlocal nonlinearity",
      "direct moving spheres method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}