  We give a new method to prove the existence, non-existence, multiplicity,
orbital stability/instability of standing waves for NLS with partial
confinement without the subcritical hypothesis, even in the reduction equation.
Using this method, we give an affirmative answer for an open problem proposed
by [7, Remark 1.10] where the authors conjectured the existence of more than a
normalized solution. We also establish uniqueness results of the ground state
solutions depending on the bifurcation parameters. We explain that when the
effect of partial confinement is strong, a dimension reduction appears for some
parameters. We also find different bifurcation phenomena from the cases with
full confinement.
