{
  "id": "1910.04815",
  "version": "v1",
  "published": "2019-10-10T19:01:42.000Z",
  "updated": "2019-10-10T19:01:42.000Z",
  "title": "Stability of solutions for nonlocal problems",
  "authors": [
    "Julián Fernández Bonder",
    "Ariel M. Salort"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we deal with the stability of solutions of fractional $p-$Laplace problems with nonlinear sources when the fractional parameter $s$ goes to 1. We prove a general convergence result for general weak solutions which is applied to study the convergence of ground state solutions of $p-$fractional problems in bounded and unbounded domains as $s$ goes to 1. Moreover, our result applies to treat the stability of $p-$fractional eigenvalues as $s$ goes to 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-10T19:01:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35B35",
      "45G05"
    ],
    "keywords": [
      "nonlocal problems",
      "ground state solutions",
      "general convergence result",
      "general weak solutions",
      "laplace problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}