{
  "id": "2407.15742",
  "version": "v1",
  "published": "2024-07-22T15:42:45.000Z",
  "updated": "2024-07-22T15:42:45.000Z",
  "title": "New solutions for the Lane-Emden problem on planar domains",
  "authors": [
    "Luca Battaglia",
    "Isabella Ianni",
    "Angela Pistoia"
  ],
  "comment": "41 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Lane-Emden problem on planar domains. When the exponent is large, the existence and multiplicity of solutions strongly depend on the geometric properties of the domain, which also deeply affect their qualitative behavior. Remarkably, a wide variety of solutions, both positive and sign-changing, have been found when the exponent is sufficiently large. In this paper, we focus on this topic and fine new sign-changing solutions that exhibit an unexpected concentration phenomenon as the exponent approaches infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-22T15:42:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35B40",
      "35B44"
    ],
    "keywords": [
      "lane-emden problem",
      "planar domains",
      "exponent approaches infinity",
      "geometric properties",
      "unexpected concentration phenomenon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}