{
  "id": "1606.02512",
  "version": "v1",
  "published": "2016-06-08T11:21:35.000Z",
  "updated": "2016-06-08T11:21:35.000Z",
  "title": "Existence and Concentration Solutions for a class of elliptic PDEs involving $p$-biharmonic Operator",
  "authors": [
    "Ratan Kr Giri",
    "Debajyoti Choudhuri",
    "Shesadev Pradhan"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we propose an existence result pertaining to a nontrivial solution to the problem \\begin{align*} \\Bigg\\{\\begin{split} & \\Delta^2_p u -\\Delta_p u + \\lambda V(x)|u|^{p-2}u = f(x,u)\\,,\\,x\\in \\mathbb{R}^N, & u \\in W^{2,p}(\\mathbb{R}^N), \\end{split} \\end{align*} where $\\lambda>0$, $p>1, N>2p$ and $V\\in C(\\mathbb{R}^N, \\mathbb{R}^+)$, $f\\in C(\\mathbb{R}^N \\times \\mathbb{R},\\mathbb{R})$ with certain properties. We also investigate the concentration of solutions to the problem on the set $V^{-1}(0)$ as $\\lambda \\rightarrow \\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-08T11:21:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J35",
      "35J60",
      "35J92"
    ],
    "keywords": [
      "biharmonic operator",
      "elliptic pdes",
      "concentration solutions",
      "nontrivial solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}