A guide to the Choquard equation

@article{Moroz2016AGT,
  title={A guide to the Choquard equation},
  author={Vitaly Moroz and Jean Van Schaftingen},
  journal={Journal of Fixed Point Theory and Applications},
  year={2016},
  volume={19},
  pages={773-813}
}
We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$\begin{aligned} -\Delta u + V(x)u = \left( |x|^{-(N-\alpha )} *|u |^p\right) |u |^{p - 2} u \quad \text {in} \ \mathbb {R}^N, \end{aligned}$$-Δu+V(x)u=|x|-(N-α)∗|u|p|u|p-2uinRN,and some of its variants and extensions. 

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