On the derivative nonlinear Schr{\"o}dinger equation on the half line with Robin boundary condition

We consider the Schr"odinger equation with nonlinear derivative term on $[0,+\mathrm{\infty })$ under Robin boundary condition at $0$. Using a virial argument, we obtain the existence of blowing up solutions and using variational techniques, we obtain stability and instability by blow up results for standing waves.