In this paper, we are concerned with the classification of positive supersolutions of the fractional Lane–Emden system

where \(p,q\in {\mathbb {R}}\) and \(0<s<1\). We prove that this system has no positive supersolution provided that \(p\le 0\) or \(q\le 0\). Consequently, this together with the results in Leite and Montenegro (Differ Integr Equ 30(11–12):947–974, 2017), Biswas (Nonlinearity 32(6):2246–2268, 2019) completes the classification of positive supersolutions of the system in the full range of p, q. On the other hand, we also provide a simple proof of the nonexistence of positive supersolutions of the system in the case \(p>0,q>0\) and \(pq\le 1\) or \(p>0,q>0,pq>1\) and \(\max \left\{ \frac{2s(p+1)}{pq-1},\frac{2s(q+1)}{pq-1}\right\} > N-2s\).

在本文中，我们关注分数Lane-Emden系统的正超解的分类

其中\（p，q \ in {\ mathbb {R}} \）和\（0 <s <1 \）。我们证明只要\（p \ le 0 \）或\（q \ le 0 \）该系统都没有正解。因此，这与Leite和Montenegro的结果（Differ Integr Equ 30（11–12）：947–974，2017），Biswas（非线性32（6）：2246–2268，2019）的结果一起完成了整个p，  q范围内的系统。另一方面，在\（p> 0，q> 0 \）和\（pq \ le 1 \）或\（p> 0，）的情况下，我们还提供了系统正超解不存在的简单证明。q> 0，pq> 1 \）和\（\ max \ left \ {\ frac {2s（p + 1）} {pq-1}，\ frac {2s（q + 1）} {pq-1} \ right \}> N-2s \）。