Scattering for the focusing $L^2$ -supercritical and ${\dot{H}}^2$-subcritical biharmonic NLS Equations

We consider the focusing ${\dot{H}}^{s_c}$-critical biharmonic Schr"odinger equation, and prove a global wellposedness and scattering result for the radial data $u_0\in H^2({\mathbb{R}}^N)$ satisfying $M(u_0{)}^{\frac{2-s_c}{s_c}}E(u_0)<M(Q{)}^{\frac{2-s_c}{s_c}}E(Q)$ and $ |u_{0}|^{\frac{2-s_c}{s_c}}{2}|\Delta u{0}|{2}<|Q|^{\frac{2-s_c}{s_c}}{2}|\Delta Q|_{2}, $where$s_c\in(0,2)$and$Q$isthegroundstateof$\Delta^2Q+(2-s_c)Q-|Q|^{p-1}Q=0$.