{
  "id": "1811.04417",
  "version": "v1",
  "published": "2018-11-11T13:47:42.000Z",
  "updated": "2018-11-11T13:47:42.000Z",
  "title": "Perturbations of nonlinear eigenvalue problems",
  "authors": [
    "Nikolaos S. Papageorgiou",
    "Vicenţiu D. Rădulescu",
    "Dušan D. Repovš"
  ],
  "journal": "Commun. Pure Appl. Anal. 18:3 (2019), 1403-1431",
  "doi": "10.3934/cpaa.2019068",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider perturbations of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator plus an indefinite potential. We consider both sublinear and superlinear perturbations and we determine how the set of positive solutions changes as the real parameter $\\lambda$ varies. We also show that there exists a minimal positive solution $\\overline{u}_\\lambda$ and determine the monotonicity and continuity properties of the map $\\lambda\\mapsto\\overline{u}_\\lambda$. Special attention is given to the particular case of the $p$-Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-11T13:47:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J60"
    ],
    "keywords": [
      "nonlinear eigenvalue problems driven",
      "nonhomogeneous differential operator plus",
      "indefinite potential",
      "special attention",
      "superlinear perturbations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}