In this paper, we investigate the following Choquard equation
$ \begin{equation*} -\Delta u = (I_\alpha*|u|^{f(x)})|u|^{f(x)-2}u \ \ \ \ {\rm in} \ \mathbb{R}^N, \end{equation*} $
where $ N\geq 3 $, $ \alpha\in (0,N) $ and $ I_\alpha $ is the Riesz potential. If
$ \begin{equation*} f(x) = \begin{cases} p, &x\in\Omega,\\ ( N+\alpha)/(N-2), &x\in\mathbb{R}^N \backslash\Omega, \end{cases} \end{equation*} $
where $ 1< p <\frac{N+\alpha}{N-2} $ and $ \Omega\subset\mathbb{R}^N $ is a bounded set with nonempty, we obtain the existence of positive ground state solutions by using the Nehari manifold.
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