The existence of positive solutions with prescribed L2-norm for nonlinear Choquard equations

By Gong-bao Li, Hongyu Ye. 2014

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Mass minimizers and concentration for nonlinear Choquard equations in $\R^N$ (2015, background): “(3) For N ≥ 3 and N+α+2 N < p < N+α N−2 , it has been proved in [9] that for each c > 0, Ip(u) has a mountain pass geometry on S(c) and there exits a couple (uc, μc) ∈ S(c)×R− solution of (1.”
Standing waves to upper critical Choquard equation with a local perturbation: Multiplicity, qualitative properties and stability (2021, unknown): “See [1, 21, 42] for studies to Choquard equation with general nonlinearity.”
Normalized solutions for the Chern–Simons–Schrödinger equation in R^2 (2017, methodology): “Under certain assumptions on G(u), by using a minimax procedure inspired by [6], the authors of [27] proved that for any c > 0, there is at least a couple (uc, λc) ∈ H(1)(R) × R− of weak solution to the equation above with ‖uc‖2 = c.”