Concentration behavior of standing waves for almost mass critical nonlinear Schrödinger equations

Yujin Guo, Xiaoyu Zeng, Huan-Song Zhou

We study the following nonlinear Schrödinger equation $$i{u}_t=-\Delta u+V(x)u-a|u{|}^{q}u(t,x)\in {\mathbb{R}}^1\times {\mathbb{R}}^2,$$ where $a>0,q\in (0,2)$ and $V(x)$ is some type…