A Liouville theorem for the fractional Ginzburg–Landau equation
- Resource Type
- article
- Authors
- Li, Yayun; Chen, Qinghua; Lei, Yutian
- Source
- Comptes Rendus. Mathématique, Vol 358, Iss 6, Pp 727-731 (2020)
- Subject
- Mathematics
QA1-939
- Language
- English
French
- ISSN
- 1778-3569
In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation \begin{equation*} u(x)=\int _{\mathbb{R}^{n}}\frac{u(1-|u|^{2})}{|x-y|^{n-\alpha }}\mathrm{d}y, \end{equation*} where $u: \mathbb{R}^{n} \rightarrow \mathbb{R}^{k}$ with $k \ge 1$ and $1