  Nonlinear Schr\"odinger equations are usually investigated with the use of
the variational methods that are limited to energy-subcritical dimensions. Here
we present the approach based on the shooting method that can give the proof of
existence of the ground states in critical and supercritical cases. We
formulate the assumptions on the system that are sufficient for this method to
work. As examples, we consider Schr\"odinger-Newton and Gross-Pitaevskii
equations with harmonic potentials.
