{
  "id": "1706.02497",
  "version": "v1",
  "published": "2017-06-08T09:56:59.000Z",
  "updated": "2017-06-08T09:56:59.000Z",
  "title": "Ground state solutions of fractional Schrödinger equations with potentials and weak monotonicity condition on the nonlinear term",
  "authors": [
    "Chao Ji"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we are concerned with the fractional Schr\\\"{o}dinger equation $(-\\Delta)^{\\alpha} u+V(x)u =f(x, u)$, $x\\in \\rn$, where $f$ is superlinear, subcritical growth and $u\\mapsto\\frac{f(x, u)}{\\vert u\\vert}$ is nondecreasing. When $V$ and $f$ are periodic in $x_{1},\\ldots, x_{N}$, we show the existence of ground states and the infinitely many solutions if $f$ is odd in $u$. When $V$ is coercive or $V$ has a bounded potential well and $f(x, u)=f(u)$, the ground states are obtained. When $V$ and $f$ are asymptotically periodic in $x$, we also obtain the ground states solutions. In the previous research, $u\\mapsto\\frac{f(x, u)}{\\vert u\\vert}$ was assumed to be strictly increasing, due to this small change, we are forced to go beyond methods of smooth analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-08T09:56:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35R11",
      "47J30"
    ],
    "keywords": [
      "fractional schrödinger equations",
      "weak monotonicity condition",
      "ground state solutions",
      "nonlinear term",
      "ground states solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}