Ground state solutions for Choquard type equations with a singular potential

This article concerns the Choquard type equation $$ -\Delta u+V(x)u=\Big(\int_{\mathbb{R}^N}\frac{|u(y)|^p}{|x-y|^{N-\alpha}}dy\Big) |u|^{p-2}u,\quad x\in \mathbb{R}^N, $$ where $N\geq3$, $\alpha\in ((N-4)_+,N)$, $2\leq p <(N+\alpha)/(N-2)$ and V(x) is a possibly singular potential and may be unbounded below. Applying a variant of the Lions' concentration-compactness principle, we prove the existence of ground state solution of the above equations