Threshold dynamics for the 3d radial NLS with combined nonlinearity

We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: ( i ∂ t + Δ ) u = | u | 2 u − | u | 4 u . In [18] , the authors classified the dynamics of solutions under the energy constraint E ( u ) < E c ( W ) , where W is the quintic NLS ground state and E c is the quintic NLS energy. In this work we classify the dynamics of H 1 solutions at the threshold E ( u ) = E c ( W ) .