Normalized Solutions for the Fractional Choquard Equations with Hardy–Littlewood–Sobolev Upper Critical Exponent

• Yuxi Meng ^[1] ; Xiaoming He ^[2]
  1. [1] Beijing Institute of Technology

     Beijing Institute of Technology

     China

     
  2. [2] Minzu University of China

     Minzu University of China

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In the present paper, we study the existence of normalized ground states for the following nonlinear fractional Choquard equations with Hardy–Littlewood–Sobolev upper critical exponent:

    (−)s u = λu + μ(Iα ∗ |u| p)|u| p−2u + (Iα ∗ |u| 2∗ α,s )|u| 2∗ α,s−2u, x ∈ RN , having prescribed mass RN |u| 2dx = a > 0, where N > 2s, s ∈ (0, 1), α ∈ (0, N), p := N+α N < p < p := N+2s+α N < 2∗ α,s, 2∗ α,s := N+α N−2s is the upper Hardy–Littlewood–Sobolev critical exponent, μ > 0 and λ ∈ R. Furthermore, the qualitative behavior of the ground states as μ → 0+ is also studied.

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