{
  "id": "1406.7415",
  "version": "v1",
  "published": "2014-06-28T15:42:29.000Z",
  "updated": "2014-06-28T15:42:29.000Z",
  "title": "Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue",
  "authors": [
    "Pedro M. Girão"
  ],
  "comment": "This is an extended version of the published paper",
  "journal": "Nonlinear Analysis: Theory, Methods & Applications 74 (2011), 94-113",
  "doi": "10.1016/j.na.2010.08.020",
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct the global bifurcation curves, solutions versus level of harvesting, for the steady states of a diffusive logistic equation on a bounded domain, under Dirichlet boundary conditions and other appropriate hypotheses, when $a$, the linear growth rate of the population, is below $\\lambda_2+\\delta$. Here $\\lambda_2$ is the second eigenvalue of the Dirichlet Laplacian on the domain and $\\delta>0$. Such curves have been obtained before, but only for $a$ in a right neighborhood of the first eigenvalue. Our analysis provides the exact number of solutions of the equation for $a\\leq\\lambda_2$ and new information on the number of solutions for $a>\\lambda_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-28T15:42:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B32",
      "35J66",
      "37B30",
      "92D25"
    ],
    "keywords": [
      "linear growth rate crosses",
      "second eigenvalue",
      "global bifurcation curves",
      "dirichlet boundary conditions",
      "diffusive logistic equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.7415G"
    }
  }
}