{
  "id": "1208.1139",
  "version": "v3",
  "published": "2012-08-06T11:42:08.000Z",
  "updated": "2013-05-20T10:10:08.000Z",
  "title": "On the second minimax level for the scalar field equation",
  "authors": [
    "Kanishka Perera",
    "Cyril Tintarev"
  ],
  "comment": "Minor revision - correction of typos. arXiv admin note: substantial text overlap with arXiv:1204.5332",
  "categories": [
    "math.AP"
  ],
  "abstract": "The paper studies eigenfunctions for the scalar field equation on $\\R^N$ at the second minimax level $\\lambda_2$. Similarly to the well-studied case of the ground state, there is a threshold level $\\lambda^#$ such that $\\lambda_2\\le \\lambda^#$, and a critical point at the level $\\lambda_2$ exists if the inequality is strict. Unlike the case of the ground state, the level $\\lambda_2$ is not attained in autonomous problems, and the existence is shown when the potential near infinity approaches the constant level from below not faster than $e^{- \\varepsilon |x|}$. The paper also considers questions about the nodal character and the symmetry breaking for solutions at the level $\\lambda_2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-05-20T10:10:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35J20",
      "47J10"
    ],
    "keywords": [
      "scalar field equation",
      "second minimax level",
      "ground state",
      "paper studies eigenfunctions",
      "nodal character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1139P"
    }
  }
}