论文标题
liouville型定理用于加权分数泳道系统的解决方案
Liouville type theorems for solutions of the weighted fractional Lane-Emden system
论文作者
论文摘要
在本文中，我们证明了liouville键入定理，以用于加权分数车道系统\ begin {align*}的稳定解决方案 （-δ） $ \ MATHBB {r}^n $满足$ \ displayStyle {\ liminf_ {| x | \ to \ frac}} \ frac {h（x）} {| x | x |^\ ell}> 0 $ 0 $ $ \ ell> 0 $ \ ell> 0。 $ s = 1 $）并改进了先前的工作\ cite {tuanhoang21}。结果，我们证明了稳定的解决方案的分类结果，用于加权分数车道方程$（-Δ）^s u = h（x）u^p $ in $ \ m asthbb {r}^n $。
In this paper, we prove Liouville type theorems for stable solutions to the weighted fractional Lane-Emden system \begin{align*} (-Δ)^s u = h(x)v^p,\quad (-Δ)^s v= h(x)u^q, \quad u,v>0\quad \mbox{in }\;\mathbb{R}^N, \end{align*} where $1<q\leq p$ and $h$ is a positive continuous function in $\mathbb{R}^N$ satisfying $\displaystyle{\liminf_{|x|\to \infty}}\frac{h(x)}{|x|^\ell} > 0$ with $\ell > 0.$ Our results generalize the results established in \cite{HHM16} for the Laplacian case (correspond to $s=1$) and improve the previous work \cite{TuanHoang21}. As a consequence, we prove classification result for stable solutions to the weighted fractional Lane-Emden equation $(-Δ)^s u = h(x)u^p$ in $\mathbb{R}^N$.
