{
  "id": "1903.07407",
  "version": "v1",
  "published": "2019-03-18T13:00:55.000Z",
  "updated": "2019-03-18T13:00:55.000Z",
  "title": "Applications of generalized trigonometric functions with two parameters",
  "authors": [
    "Hiroyuki Kobayashi",
    "Shingo Takeuchi"
  ],
  "comment": "19 pages, 2 figures",
  "journal": "Commun. Pure Appl. Anal. 18 (2019), no.3, 1509-1521",
  "doi": "10.3934/cpaa.2019072",
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator, and there are a lot of works on GTFs concerning the $p$-Laplacian. However, few applications to differential equations unrelated to the $p$-Laplacian are known. We will apply GTFs with two parameters to nonlinear nonlocal boundary value problems without $p$-Laplacian. Moreover, we will give integral formulas for the functions, e.g. Wallis-type formulas, and apply the formulas to the lemniscate function and the lemniscate constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-18T13:00:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized trigonometric functions",
      "parameters",
      "nonlinear nonlocal boundary value problems",
      "applications",
      "typical nonlinear differential operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}