  We consider the nonlinear Schr\"odinger equation with focusing quintic and
defocusing cubic nonlinearity in three space dimensions: \[
(i\partial_t+\Delta)u = |u|^2 u - |u|^4 u. \] In [18, 23], 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 $E(u)=E^c(W)$.

Analysis of PDEs