  In this paper, we establish the existence of ground state solutions for
Choquard equations \begin{equation}\label{eq 1}
  - \Delta u + u = q\,(I_\alpha \ast |u|^p) |u|^{q - 2} u+p\,(I_\alpha \ast
|u|^q) |u|^{p - 2} u\quad {\rm in }\quad \mathbb{R}^N, \end{equation} where $N
\ge 3$, $\alpha \in (0, N)$, $I_\alpha: \mathbb{R}^N \to \mathbb{R}$ is the
Riesz potential, $p,\,q >0$ satisfying that \begin{equation}\label{eq 2}
\frac{2(N+\alpha)}{N}<p+q< \frac{2(N+\alpha)}{N-2}. \end{equation} Moreover, we
prove a Poho\v{z}aev type identity for this Choquard equation, which implies
the non-existence result for the problem when $(p,q)$ does not satisfy the
above condition.
