Normalized solutions for Choquard equations with critical nonlinearities on bounded domains

2025/06/23 by Yan, Ru
#35B38 #35J20 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.19872

Abstract

The aim of this work is the study of the existence of normalized solutions to the nonlinear Schrödinger equation with nonlocal nonlinearities: \\beginaligned amp;-Δu =λu+(I_α*|u|^{2_α^*})|u|^{2_α^*-2}u+a(I_α*|u|^p)|u|^p-2u, x∈Ω,
amp;ugt;0 \text in Ω, u=0 \text on ∂ Ω, ∫ _Ω|u|²dx=c, \endaligned . where c>0, α∈ (0,N), (N+α+2)/(N)

Citations

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• Normalized solutions to a Choquard equation involving mixed local and nonlocal operators