# 数学学院、所2020年系列学术活动（第247场）：雷雨田 教授 南京师范大学

https://meeting.tencent.com/s/zjWCpX21WUsF

In this talk, we will introduce a Liouville-type result of the nonlinear integral equation\begin{equation*}u(x)=\overrightarrow{l}+C_*\int_{\mathbb{R}^{n}}\frac{u(1-|u|^{2})}{|x-y|^{n-\alpha}}dy.\end{equation*}Here $u: \mathbb{R}^{n} \to \mathbb{R}^{k}$ is a bounded, uniformly continuous and differentiable function with $k \geq 1$ and $1<\alpha<n$, $\overrightarrow{l} \in \mathbb{R}^{k}$ is a constant vector, and $C_*$ is a real constant. If $u$ is the finite energy solution, we will prove that $|\overrightarrow{l}| \in \{0,1\}$. Furthermore, we also give a Liouville type theorem (i.e., $u \equiv \overrightarrow{l}$).