ON THE DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION ON THE HALF LINE WITH ROBIN BOUNDARY CONDITION

Phan van Tin (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider the Schr\"odinger equation with nonlinear derivative term on $[0,+\infty)$ 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.

Domaines: Equations aux dérivées partielles [math.AP]

Phan van Tin. ON THE DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION ON THE HALF LINE WITH ROBIN BOUNDARY CONDITION. 2021. ⟨hal-03024660v7⟩