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

Yuxi Meng, Xiaoming He

• 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.