Liouville type theorem for some Choquard type equation

In this paper, we study the nonexistence result of positive solution for the following Choquard equation: $$-\Delta u=\int_{ \mathbb R^N} \frac{F(u(y))}{|x-y|^{N-\alpha}}dy f(u(x)), x\in \mathbb R^N, $$ where $N\geq 3$ is the dimension of the space. Under some assumptions on $F$ and $f$, we prove that the above equation does not possess nontrivial positive solution. We use the moving plane method in an integral form to prove this result.