Existence theorems for a class of systems involving two quasilinear operators

In this paper, we study the existence of positive radial solutions for a class of quasilinear systems of the form
$$ \begin{cases} \Delta_{\phi_1}u=a_1(|x|)f_1(v), \\ \Delta_{\phi_2}v=a_2(|x|)f_2(u), \end{cases} \quad x\in \mathbb{R}^N, \quad N\geqslant 3, $$
where $\Delta_{\phi}w:=\operatorname{div}(\phi(|\nabla w|)\nabla w)$, under appropriate conditions on the functions $\phi_1$, $\phi_2$, the weights $a_1$, $a_2$ and the non-linearities $f_1$, $f_2$. The conditions imposed for the existence of such solutions are different from those in previous results.