Bidaut-Véron–Szulkin conjecture for the Hamiltonian system

Consider the Hamiltonian system

$$(SH)\left\{\begin{array}{c}-\Delta u=\left\vert x\right\vert ^a v^\delta,\\-\Delta v=\left\vert x\right\vert ^b u^\mu,\end{array}\right.$$

with $p=q=2<N$, $s=m=0$, and $a>-2$. In the case $a=b=0$, the relevant exponents are $(\delta,\mu)$.

Bidaut-Véron–Szulkin conjecture. System $(SH)$ with $a=b=0$ admits no radial or nonradial global solutions if and only if $(\delta,\mu)$ lies under the hyperbola

$$\frac{N}{\delta+1}+\frac{N}{\mu+1}=N-2.$$

The question was open in the source; it had been solved in the radial case, partially in subsequent work, and up to dimension $N=4$, while the general nonradial case remained unresolved.