{
  "id": "1311.3587",
  "version": "v2",
  "published": "2013-11-14T17:28:36.000Z",
  "updated": "2013-12-20T03:10:41.000Z",
  "title": "A multiplicity result for the scalar field equation",
  "authors": [
    "Kanishka Perera"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence of $N - 1$ distinct pairs of nontrivial solutions of the scalar field equation in ${\\mathbb R}^N$ under a slow decay condition on the potential near infinity, without any symmetry assumptions. Our result gives more solutions than the existing results in the literature when $N \\ge 6$. When the ground state is the only positive solution, we also obtain the stronger result that at least $N - 1$ of the first $N$ minimax levels are critical, i.e., we locate our solutions on particular energy levels with variational characterizations. Finally we prove a symmetry breaking result when the potential is radial. To overcome the difficulties arising from the lack of compactness we use the concentration compactness principle of Lions, expressed as a suitable profile decomposition for critical sequences.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-20T03:10:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35P30",
      "35J20"
    ],
    "keywords": [
      "scalar field equation",
      "multiplicity result",
      "slow decay condition",
      "concentration compactness principle",
      "distinct pairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.3587P"
    }
  }
}