Local and global well-posedness for the nonlinear Schrödinger equation with nonhomogeneous boundary conditions

Engui Fan, Yuan Li, Xinhan Liu

In this paper, we study the initial-boundary value problem for the nonlinear Schrödinger equation in ${\mathbb{R}}_{+}^n$ \begin{equation*} i\partial_{t}u+Δu+λ|u|^pu=0, \qquad (x,…