论文标题
liouville type定理用于分数椭圆问题
Liouville type theorems for fractional elliptic problems
论文作者
论文摘要
在本文中，我们为整个空间上的稳定解决方案建立liouville type定理$ \ mathbb r^n $ to ktractional椭圆方程 $$（ - δ）^su = f（u）$$，在非线性不稳定和凸。我们还获得了分数泳道系统稳定解决方案的分类 $$ \ begin {case} （-Δ）^s u = v^p \ mbox {in} \ mathbb r^n （-δ）^s v = u^q \ mbox {in} \ mathbb r^n \ end {case} $$ $ p> 1 $和$ q> 1 $。据我们所知，这是文献中稳定解决方案稳定解决方案的第一个分类结果。
In this paper, we establish Liouville type theorems for stable solutions on the whole space $\mathbb R^N$ to the fractional elliptic equation $$(-Δ)^su=f(u)$$ where the nonlinearity is nondecreasing and convex. We also obtain a classification of stable solutions to the fractional Lane-Emden system $$\begin{cases} (-Δ)^s u = v^p \mbox{ in }\mathbb R^N (-Δ)^s v = u^q \mbox{ in }\mathbb R^N \end{cases}$$ with $p>1$ and $ q>1$. In our knowledge, this is the first classification result for stable solutions of the fractional Lane-Emden system in literature.
