Strong instability of ground states to a fourth order Schr\"odinger equation

In this note we prove the instability by blow-up of the ground state solutions for a class of fourth order Schr" odinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic NLS due to Boulenger and Lenzmann \cite{BoLe} and confirm numerical conjectures from \cite{BaFi, BaFiMa1, BaFiMa, FiIlPa}.