{
  "id": "1703.02450",
  "version": "v1",
  "published": "2017-03-07T16:07:05.000Z",
  "updated": "2017-03-07T16:07:05.000Z",
  "title": "Existence and multiplicity result for a fractional p-Laplacian equation with combined fractional derivatives",
  "authors": [
    "César Torres",
    "Nemat Nyamoradi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The aim of this paper is to obtain the existence of solutions for the following fractional p-Laplacian Dirichlet problem with mixed derivatives \\begin{eqnarray*} &{_{t}}D_{T}^{\\alpha}\\left(|_{0}D_{t}^{\\alpha}u(t)|^{p-2}{_{0}}D_{t}^{\\alpha}u(t)\\right) = f(t, u(t)), \\;t\\in [0,T],\\\\ &u(0) = u(T) = 0, \\end{eqnarray*} where $0 < \\alpha <1$, $1<p<\\infty$ and $f:[0,T]\\times \\mathbb{R} \\to \\mathbb{R}$ is a continuous function. We obtain the existence of nontrivial solutions by using the direct method in variational methods and the genus in the critical point theory. Furthermore, if $0< \\alpha < \\frac{1}{p}$ we obtain an almost every where classical solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-07T16:07:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "35A15",
      "35B38"
    ],
    "keywords": [
      "fractional p-laplacian equation",
      "multiplicity result",
      "fractional derivatives",
      "fractional p-laplacian dirichlet problem",
      "direct method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}