One-dimensional symmetry of positive bounded solutions to the subcubic and cubic nonlinear Schrödinger equation in the half-space in dimensions $N=4,5$

Christos Sourdis

We are concerned with the half-space Dirichlet problem \[\left\{\begin{array}{ll} -Δv+v=|v|^{p-1}v & \textrm{in}\ \mathbb{R}^N_+, v=c\ \textrm{on}\ \partial\mathbb{R}^N_+, &\lim_{x…