  We are going to study the standing waves for a generalized Choquard equation
with potential: $$ -i\partial_t u-\Delta
u+V(x)u=(|x|^{-\mu}\ast|u|^p)|u|^{p-2}u, \ \ \hbox{in}\ \
\mathbb{R}\times\mathbb{R}^3, $$ where $V(x)$ is a real function, $0<\mu<3$,
$2-\mu/3<p<6-\mu$ and $\ast$ stands for convolution. Under suitable assumptions
on the potential and appropriate frequency $\omega$ , the stability and
instability of the standing waves $u=e^{i \omega t}\varphi(x)$ are investigated .

Analysis of PDEs