Stability and instability of standing waves for a generalized Choquard equation with potential

Zhipeng Cheng, Minbo Yang

We are going to study the standing waves for a generalized Choquard equation with potential: $$ -i\partial_t u-Δu+V(x)u=(|x|^{-μ}\ast|u|^p)|u|^{p-2}u, \ \ \hbox{in}\ \ \mathbb{R}\t…