{
  "id": "1402.6838",
  "version": "v1",
  "published": "2014-02-27T09:50:24.000Z",
  "updated": "2014-02-27T09:50:24.000Z",
  "title": "Multi-bump solutions for a class of quasilinear problems involving variable exponents",
  "authors": [
    "Claudianor O. Alves",
    "Marcelo C. Ferreira"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish the existence of multi-bump solutions for the following class of quasilinear problems $$ - \\Delta_{ p(x) } u + \\big( \\lambda V(x) + Z(x) \\big) u ^{ p(x)-1 } = f(x,u) \\text{ in } \\mathbb R^N, \\, u \\ge 0 \\text{ in } \\mathbb R^N, $$ where the nonlinearity $ f \\colon \\mathbb R^N \\times \\mathbb R \\to \\mathbb R $ is a continuous function having a subcritical growth and potentials $ V, Z \\colon \\mathbb R^N \\to \\mathbb R $ are continuous functions verifying some hypotheses. The main tool used is the variational method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-27T09:50:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasilinear problems",
      "multi-bump solutions",
      "variable exponents",
      "continuous function",
      "main tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.6838A"
    }
  }
}