{
  "id": "2108.00711",
  "version": "v1",
  "published": "2021-08-02T08:28:35.000Z",
  "updated": "2021-08-02T08:28:35.000Z",
  "title": "Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs",
  "authors": [
    "Bobo Hua",
    "Wendi Xu"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "In this paper, we study the nonlinear Schr\\\"{o}dinger equation $ -\\Delta u+V(x)u=f(x,u) $on the lattice graph $ \\mathbb{Z}^{N}$. Using the Nehari method, we prove that when $f$ satisfies some growth conditions and the potential function $V$ is periodic or bounded, the above equation admits a ground state solution. Moreover, we extend our results from $\\mathbb{Z}^{N}$ to quasi-transitive graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-02T08:28:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "39A14",
      "58E30"
    ],
    "keywords": [
      "ground state solution",
      "nonlinear schrödinger equations",
      "lattice graph",
      "growth conditions",
      "potential function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}