Instability of standing waves for inhomogeneous Hartree equations

We are concerned with the instability of standing-wave solutions e(iota omega t)phi(omega)(x) to the Hartree equation iu(t) + Delta u + gu(vertical bar.vertical bar(-gamma) * (g vertical bar u vertical bar(2))) = 0 for some suitable g(x), where cow is a ground state solution. The instability of standing-wave solutions reveals a balance between omega and gamma. (C) 2016 Elsevier Inc. All rights reserved.