Radial symmetry of positive solutions to quasilinear Hardy-Sobolev doubly critical systems

The aim of this paper is to prove radial symmetry results for positive weak solutions with finite energy to the following quasilinear doubly critical system \begin{equation} \begin{cases} -Δ_p u,=γ\frac{u^{p-1}}{|x|^p} + u^{p^-1}+ ναu^{α-1} v^β& $\text{in}$\quad $\mathbb{R}$^n \ -Δ_p v,=γ\frac{v^{p-1}}{|x|^p} + v^{p^-1}+ νβu^αv^{β-1} & $\text{in}$\quad$\mathbb{R}$^n, \end{cases} \end{equation} where $1<p<n$, $\gamma \in [0,{\mathrm{\Lambda }}_{n,p})$ with ${\mathrm{\Lambda }}_{n,p}={[(n-p)\mathrm{/}p]}^p$, $\alpha ,\beta >1$ such that $\alpha +\beta =p^{\ast }=np\mathrm{/}(n-p)$ and $\nu >0$.