Standing waves for defocusing nonlinear Schrödinger equations with point interaction

Noriyoshi Fukaya, Yuki Osada, Mario Rastrelli

We consider standing waves of the nonlinear Schrödinger equation $i{\partial }_{t}u=-{\Delta }_{\alpha }u+|u{|}^{p-1}u$ in the defocusing case in dimensions $N=2$ and $N=3$. Here, $-{\Delta }_{\alpha }$ denotes the…