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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.

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