{
  "id": "2210.08513",
  "version": "v1",
  "published": "2022-10-16T11:49:23.000Z",
  "updated": "2022-10-16T11:49:23.000Z",
  "title": "The ground state solutions of nonlinear Schrödinger equations with Hardy weights on lattice graphs",
  "authors": [
    "Lidan Wang"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the nonlinear Schr\\\"{o}dinger equation $$ -\\Delta u+(V(x)- \\frac{\\rho}{(|x|^2+1)})u=f(x,u) $$ on the lattice graph $\\mathbb{Z}^N$ with $N\\geq 3$, where $V$ is a bounded periodic potential and $0$ lies in a spectral gap of the Schr\\\"{o}dinger operator $-\\Delta+V$. Under some assumptions on the nonlinearity $f$, we prove the existence and asymptotic behavior of ground state solutions with small $\\rho\\geq 0$ by the generalized linking theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-16T11:49:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35A15",
      "35B40",
      "35R02",
      "G.2"
    ],
    "keywords": [
      "ground state solutions",
      "nonlinear schrödinger equations",
      "lattice graph",
      "hardy weights",
      "bounded periodic potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}