Instability of standing waves for inhomogeneous Hartree equations

We are concerned with the instability of standing-wave solutions eiωtφω(x)eiωtφω(x) to the Hartree equation iut+Δu+gu(|⋅|−γ⁎(g|u|2))=0iut+Δu+gu(|⋅|−γ⁎(g|u|2))=0 for some suitable g(x)g(x), where φωφω is a ground state solution. The instability of standing-wave solutions reveals a balance between ω and γ.