Concentration behaviour of normalized ground states of the mass critical fractional Schrödinger equations with ring-shaped potentials

作者：Lintao Liu, Kaimin Teng, Jie Yang, Haibo Chen · 发表于：Proceedings of the Royal Society of Edinburgh Section A Mathematics · 年份：2022 · DOI：10.1017/prm.2022.81 · 被引用次数：4 · 研究领域：Nonlinear Partial Differential Equations、Advanced Mathematical Physics Problems、Numerical methods in inverse problems

We consider $L^{2}$ -constraint minimizers of the mass critical fractional Schrödinger energy functional with a ring-shaped potential $V(x)=(|x|-M)^{2}$ , where $M>0$ and $x\in \mathbb {R}^{2}$ . By analysing some new estimates on the least energy of the mass critical fractional Schrödinger energy functional, we obtain the concentration behaviour of each minimizer of the mass critical fractional Schrödinger energy functional when $a\nearrow a^{\ast }=\|Q\|_{2}^{2s}$ , where $Q$ is the unique positive radial solution of $(-\Delta )^{s}u+su-|u|^{2s}u=0$ in $\mathbb {R}^{2}$ .