{
  "id": "2301.12205",
  "version": "v1",
  "published": "2023-01-28T13:58:59.000Z",
  "updated": "2023-01-28T13:58:59.000Z",
  "title": "On a class of infinite semipositone problems for (p,q) Laplace operator",
  "authors": [
    "R. Dhanya",
    "R. Harish",
    "Sarbani Pramanik"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We analyze a non-linear elliptic boundary value problem, that involves $(p, q)$ Laplace operator, for the existence of its positive solution in an arbitrary smooth bounded domain. The non-linearity here is driven by a continuous function in $(0,\\infty)$ which is singular, monotonically increasing and eventually positive. We prove the existence of a positive solution of this problem using a fixed point theorem due to Amann\\cite{amann1976fixed}. In addition, for a specific nonlinearity we derive that the obtained solution is maximal in nature. The main results obtained here are first of its kind for a $(p, q)$ Laplace operator in an arbitrary bounded domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-28T13:58:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A15",
      "35B33",
      "35R11",
      "35J20"
    ],
    "keywords": [
      "laplace operator",
      "infinite semipositone problems",
      "non-linear elliptic boundary value problem",
      "positive solution",
      "arbitrary smooth bounded domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}