{
  "id": "2303.10830",
  "version": "v1",
  "published": "2023-03-20T02:27:02.000Z",
  "updated": "2023-03-20T02:27:02.000Z",
  "title": "Positive ground state solutions for generalized quasilinear Schrödinger equations with critical growth",
  "authors": [
    "Xin Meng",
    "Shuguan Ji"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "This paper concerns the existence of positive ground state solutions for generalized quasilinear Schr\\\"odinger equations in $\\mathbb{R}^N$ with critical growth which arise from plasma physics, as well as high-power ultrashort laser in matter. By applying a variable replacement, the quasilinear problem reduces to a semilinear problem which the associated functional is well defined in the Sobolev space $H^1(\\mathbb{R}^N)$. We use the method of Nehari manifold for the modified equation, establish the minimax characterization, then obtain each Palais-Smale sequence of the associated energy functional is bounded. By combining Lions's concentration-compactness lemma together with some classical arguments developed by Br\\'ezis and Nirenberg \\cite{bn}, we establish that the bounded Palais-Smale sequence has a nonvanishing behaviour. Finally, we obtain the existence of a positive ground state solution under some appropriate assumptions. Our results extend and generalize some known results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-20T02:27:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive ground state solution",
      "generalized quasilinear schrödinger equations",
      "critical growth",
      "palais-smale sequence",
      "quasilinear problem reduces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}