{
  "id": "2109.10289",
  "version": "v1",
  "published": "2021-09-21T16:10:46.000Z",
  "updated": "2021-09-21T16:10:46.000Z",
  "title": "Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems",
  "authors": [
    "Ricardo Lima Alves"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter $\\lambda>0$ varies. In our first result, the superlinear perturbation has an arbitrary growth and we obtain the existence of a solution for the problem by using the sub-supersolution method. For the second result, the superlinear perturbation has subcritical growth and we employ the Mountain Pass Theorem to show the existence of a second solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-21T16:10:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular quasilinear problems",
      "positive solutions",
      "multiplicity",
      "nonexistence",
      "parametric superlinear perturbation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}