Orbital Stability of Standing Waves for Fractional Hartree Equation with Unbounded Potentials

Jian Zhang, Shijun Zheng, Shihui Zhu

We prove the existence of the set of ground states in a suitable energy space ${\Sigma }^s=\{u:{\int }_{{\mathbb{R}}^N}\bar{u}(-\Delta +m^2{)}^{s}u+V|u{|}^2<\infty \}$, $s\in (0,\frac{N}{2})$ for the ma…