Abstract In this paper, we study the existence of positive solutions to the following nonlocal elliptic systems
$$
\cases
- M_1\left(\int_\Omega |\nabla u|^p\,dx\right)\Delta_p u = \alpha_1 a(x)f_1(v) + \beta_1b(x)g_1(u), \quad x \in \Omega,\\
- M_2\left(\int_\Omega |\nabla v|^q\,dx\right)\Delta_q v = \alpha_2 c(x)f_2(u) + \beta_2d(x)g_2(v), \quad x \in \Omega,\\
u = v = 0, \quad x \in \partial\Omega,
\endcases
$$
where $\Omega$ is a bounded domain in $\Bbb{R}^N$ with smooth boundary $\partial\Omega$, $1 ![Creative Commons License](https://i.creativecommons.org/l/by/4.0/80x15.png)
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