{
  "id": "1202.4654",
  "version": "v2",
  "published": "2012-02-21T14:51:14.000Z",
  "updated": "2012-02-23T08:19:20.000Z",
  "title": "Bifurcation along curves for the p-Laplacian with radial symmetry",
  "authors": [
    "François Genoud"
  ],
  "comment": "Minor changes to the statement and proof of Theorem 11",
  "journal": "Electron. J. Diff. Equ. 2012 (2012), No. 124",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the global structure of the set of radial solutions of a nonlinear Dirichlet problem involving the p-Laplacian with p>2, in the unit ball of $R^N$, $N \\ges 1$. We show that all non-trivial radial solutions lie on smooth curves of respectively positive and negative solutions and bifurcating from the line of trivial solutions. This involves a local bifurcation result of Crandall-Rabinowitz type, and global continuation arguments relying on monotonicity properties of the equation. An important part of the analysis is dedicated to the delicate issue of differentiability of the inverse p-Laplacian. We thus obtain a complete description of the global continua of positive/negative solutions bifurcating from the first eigenvalue of a weighted, radial, p-Laplacian problem, by using purely analytical arguments, whereas previous related results were proved by topological arguments or a mixture of analytical and topological arguments. Our approach requires stronger hypotheses but yields much stronger results, bifurcation occuring along smooth curves of solutions, and not only connected sets.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-23T08:19:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J66",
      "35J92",
      "35B32"
    ],
    "keywords": [
      "radial symmetry",
      "non-trivial radial solutions lie",
      "smooth curves",
      "nonlinear dirichlet problem",
      "local bifurcation result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.4654G"
    }
  }
}