{
  "id": "2305.01705",
  "version": "v1",
  "published": "2023-05-02T18:15:37.000Z",
  "updated": "2023-05-02T18:15:37.000Z",
  "title": "Infinitely many solutions for $p$-fractional Choquard type equations involving general nonlocal nonlinearities with critical growth via the concentration compactness method",
  "authors": [
    "Masaki Sakuma"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence of infinitely many solutions to a fractional Choquard type equation \\[ (-\\Delta)^s_p u+V(x)|u|^{p-2}u=(K\\ast g(u))g'(u)+\\varepsilon_W W(x)f'(u)\\quad\\text{in }\\mathbb{R}^N \\] involving fractional $p$-Laplacian and a general convolution term with critical growth. In order to obtain infinitely many solutions, we use a type of the symmetric mountain pass lemma which gives a sequence of critical values converging to zero for even functionals. To assure the $(PS)_c$ conditions, we also use a nonlocal version of the concentration compactness lemma.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-02T18:15:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional choquard type equation",
      "general nonlocal nonlinearities",
      "concentration compactness method",
      "critical growth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}