Complex-valued Solutions of the Planar Schrödinger-Newton System

2023/04/22 by Zhang, Hongfei, Zhang, Shu
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.11308

Abstract

In this paper, we consider complex-valued solutions of the planar Schrödinger-Newton system, which can be described by minimizers of the constraint minimization problem. It is shown that there exists a critical rotational velocity 0<Ω^*≤ ∞, depending on the general trapping potential V(x), such that for any rotational velocity 0≤Ω<Ω^*, minimizers exist if and only if 00 is the unique positive solution of -Δu+u-u³=0 in ℝ². Moreover, under some suitable assumptions on V(x), applying blow-up analysis and energy estimates, we present a detailed analysis on the concentration behavior of minimizers as a\nearrow a^*.

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