  We study charged and radially excited boson stars in both asymptotically flat
as well as asymptotically Anti-de Sitter space-time. We demonstrate that two
different types of radially excited solutions exist~: one that persists in the
linear limit of small scalar fields, in which analytical arguments suggest the
existence of these solutions, and one that appears only in the highly
non-linear regime of the model. We also demonstrate that the formation of wavy
scalar hair discussed previously for black holes and boson stars in
asymptotically flat space-time persists for asymptotically Anti-de Sitter
space-time.
