Orbital instability of standing waves for the generalized 3d nonlocal nonlinear schrödinger equations

The existence and orbital instability of standing waves for the generalized three-dimensional nonlocal nonlinear Schrödinger equations is studied. By defining some suitable functionals and a constrained variational problem, we first establish the existence of standing waves, which relys on the inner structure of the equations under consideration to overcome the drawback that nonlocal terms violate the space-scale invariance. We then show the orbital instability of standing waves. The arguments depend upon the conservation laws of the mass and of the energy.