{
  "id": "1012.5428",
  "version": "v5",
  "published": "2010-12-24T20:03:36.000Z",
  "updated": "2015-08-29T17:01:51.000Z",
  "title": "Multiplicity and regularity of periodic solutions for a class of degenerate semilinear wave equations",
  "authors": [
    "Jean Marcel Fokam"
  ],
  "comment": "Lemma 1.1 in previous version had a mistake",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations: \\[ u_{tt}-u_{xx}+|u|^{s-1}u=f(x,t), \\] for all $s>1$. In particular we prove the existence of infinitely many classical solutions for the case $s=3$ posed by Br\\'ezis in \\cite{BrezisBAMS}. The proof relies on a new upper a priori estimates for minimax values of, a pertubed from symmetry, strongly indefinite functional,depending on a small parameter.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-06-22T03:41:48.000Z",
      "comment": "Previous version had a computationl error in section 1 and a mistake in section 2",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-08-29T17:01:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A15",
      "35Jxx",
      "35B45",
      "35L05",
      "35B10",
      "42B35",
      "34C25"
    ],
    "keywords": [
      "degenerate semilinear wave equations",
      "multiplicity",
      "regularity",
      "classical periodic solutions",
      "proof relies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.5428M"
    }
  }
}