A new critical curve for the Lane-Emden system

We study stable positive radially symmetric solutions for the Lane-Emden system $-\mathrm{\Delta }u=v^p$ in ${\mathbb{R}}^N$, $-\mathrm{\Delta }v=u^q$ in ${\mathbb{R}}^N$, where $p,q\ge 1$. We obtain a new critical curve that optimally describes the existence of such solutions.