{
  "id": "1303.4345",
  "version": "v1",
  "published": "2013-03-18T18:05:09.000Z",
  "updated": "2013-03-18T18:05:09.000Z",
  "title": "A Sufficient Condition for the Existence of a Principal Eigenvalue for Nonlocal Diffusion Equations with Applications",
  "authors": [
    "Daniel B. Smith"
  ],
  "categories": [
    "math.FA",
    "math.AP",
    "math.DS"
  ],
  "abstract": "Considerable work has gone into studying the properties of nonlocal diffusion equations. The existence of a principal eigenvalue has been a significant portion of this work. While there are good results for the existence of a principal eigenvalue equations on a bounded domain, few results exist for unbounded domains. On bounded domains, the Krein-Rutman theorem on Banach spaces is a common tool for showing existence. This article shows that generalized Krein-Rutman can be used on unbounded domains and that the theory of positive operators can serve as a powerful tool in the analysis of nonlocal diffusion equations. In particular, a useful sufficient condition for the existence of a principal eigenvalue is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-18T18:05:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlocal diffusion equations",
      "applications",
      "unbounded domains",
      "principal eigenvalue equations",
      "significant portion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4345S"
    }
  }
}