Strong instability of standing waves for a nonlocal Schrödinger equation

Variational methods are used to prove that the solutions of the nonlocal Schrödinger equation iφt+△φ+φ|φ|p−2(V(x)∗|φ|p)=0,x∈RN must blow up for a class of initial data with nonnegative energy and some restriction on pp. Then using this we prove that the standing wave must be H1(RN)H1(RN) strongly unstable with respect to the nonlocal nonlinear Schrödinger equation.