Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space

We consider the inhomogeneous Dirichlet-boundary value problem for nonlinear Schrödinger equations with a power nonlinearity in general space dimension $$n\ge 3$$ n ≥ 3 . We present some results on global existence in time and uniquness of small solutions to integral equations associated to the original problem.