New result on Lane-Emden conjecture with exponents in a disk

We obtain new results on Lane-Emden conjecture to prove a Liouville theorem for the Lane-Emden system $$\begin{cases} -Δu=v^p,& x\in \mathbb{R}^N,\\ -Δv=u^q,& x\in \mathbb{R}^N,\end{cases}$$ with $N\ge3$, $p,q>0$, $pq>1$, and \[ \left(p-\frac2{N-2}\right)^2+ \left(q-\frac2{N-2}\right)^2\le\frac{2N^2