论文标题
liouville定理，用于分数金茨堡 - 兰道等式
A Liouville theorem for the fractional Ginzburg-Landau equation
论文作者
论文摘要
在本文中，我们关注的是非线性积分方程的liouville型结果\ begin {equation*} u（x）= \ int _ {\ mathbb {\ mathbb {r}^{n}}} \ frac {u（1- | |^{2}}} $ u：\ mathbb {r}^{n} \ to \ mathbb {r}^{k} $带有$ k \ geq 1 $和$ 1 <α<n/2 $。我们证明，只要$ u $是一个有界的和可区分的解决方案，$ u \ in l^2（\ mathbb {r}^n）\ rightarrow u \ equiv 0 $ 0 $。
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-α}}dy, \end{equation*} where $u: \mathbb{R}^{n} \to \mathbb{R}^{k}$ with $k \geq 1$ and $1<α<n/2$. We prove that $u \in L^2(\mathbb{R}^n) \Rightarrow u \equiv 0$ on $\mathbb{R}^n$, as long as $u$ is a bounded and differentiable solution.
