{
  "id": "2205.09535",
  "version": "v1",
  "published": "2022-05-19T12:59:44.000Z",
  "updated": "2022-05-19T12:59:44.000Z",
  "title": "Anisotropic singular Neumann equations with unbalanced growth",
  "authors": [
    "Nikolaos S. Papageorgiou",
    "Vicenţiu D. Rădulescu",
    "Dušan D. Repovš"
  ],
  "journal": "Potential Anal. 57:1 (2022), 55-82",
  "doi": "10.1007/s11118-021-09905-4",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a nonlinear parametric Neumann problem driven by the anisotropic $(p,q)$-Laplacian and a reaction which exhibits the combined effects of a singular term and of a parametric superlinear perturbation. We are looking for positive solutions. Using a combination of topological and variational tools together with suitable truncation and comparison techniques, we prove a bifurcation-type result describing the set of positive solutions as the positive parameter $\\lambda$ varies. We also show the existence of minimal positive solutions $u_\\lambda^*$ and determine the monotonicity and continuity properties of the map $\\lambda\\mapsto u_\\lambda^*$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-19T12:59:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J75",
      "35J60",
      "35J20"
    ],
    "keywords": [
      "anisotropic singular neumann equations",
      "unbalanced growth",
      "nonlinear parametric neumann problem driven",
      "positive solutions",
      "parametric superlinear perturbation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}