{
  "id": "1704.02131",
  "version": "v1",
  "published": "2017-04-07T08:35:57.000Z",
  "updated": "2017-04-07T08:35:57.000Z",
  "title": "A characterization related to Schrödinger equations on Riemannian manifolds",
  "authors": [
    "Francesca Faraci",
    "Csaba Farkas"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we consider the following problem $$\\begin{cases} -\\Delta_{g}u+V(x)u=\\lambda\\alpha(x)f(u), & \\mbox{in }M\\\\ u\\geq0, & \\mbox{in }M\\\\ u\\to0, & \\mbox{as }d_{g}(x_{0},x)\\to\\infty \\end{cases}$$where $(M,g)$ is a $N$-dimensional ($N\\geq3)$, non-compact Riemannian manifold with asymptotically non-negative Ricci curvature, $\\lambda$ is a real parameter, $V$ is a positive coercive potential, $\\alpha$ is a bounded function and $f$ is a suitable nonlinearity. By using variational methods we prove a characterization result for existence of solutions for our problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-07T08:35:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger equations",
      "non-compact riemannian manifold",
      "real parameter",
      "characterization result",
      "variational methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}