Mass concentration and uniqueness of ground states for mass subcritical rotational nonlinear Schrödinger equations

2021/12/27 by Gao, Yongshuai, Luo, Yong
#35J20 #35Q40 #46N50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.13633

Abstract

This paper considers ground states of mass subcritical rotational nonlinear Schrödinger equation -Δu+V(x)u+iΩ(x^⊥⋅∇ u)=μu+ρ^p-1|u|^p-1u in ℝ², where V(x) is an external potential, Ω>0 characterizes the rotational velocity of the trap V(x), 10 describes the strength of the attractive interactions. It is shown that ground states of the above equation can be described equivalently by minimizers of the L²- constrained variational problem. We prove that minimizers exist for any ρ∈(0,∞) when 0Ω^*, there admits no minimizers for any ρ∈(0,∞). For fixed 00 is large enough and Ω∈(0,Ω^*) is fixed.

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