Strong instability of standing waves for a nonlocal Schrِdinger equation

Variational methods are used to prove that the solutions of the nonlocal Schrödinger equation i φ t + △ φ + φ | φ | p − 2 ( V ( x ) ∗ | φ | p ) = 0 , x ∈ R N must blow up for a class of initial data with nonnegative energy and some restriction on p . Then using this we prove that the standing wave must be H 1 ( R N ) strongly unstable with respect to the nonlocal nonlinear Schrödinger equation.