  Excited states are stationary localized solutions of the Gross--Pitaevskii
equation with a harmonic potential and a repulsive nonlinear term that have
zeros on a real axis. Existence and asymptotic properties of excited states are
considered in the semi-classical (Thomas-Fermi) limit. Using the method of
Lyapunov--Schmidt reductions and the known properties of the ground state in
the Thomas--Fermi limit, we show that excited states can be approximated by a
product of dark solitons (localized waves of the defocusing nonlinear
Schr\"{o}dinger equation with nonzero boundary conditions) and the ground
state. The dark solitons are centered at the equilibrium points where a balance
between the actions of the harmonic potential and the tail-to-tail interaction
potential is achieved.
