  The stationary solutions of the Gross-Pitaevskii equation can be divided in
two classes: those which reduce, in the limit of vanishing nonlinearity, to the
eigenfunctions of the associated Schr\"odinger equation and those which do not
have linear counterpart. Analytical and numerical results support an existence
condition for the solutions of the first class in terms of the ratio between
their proper frequency and the corresponding linear eigenvalue. For
one-dimensional confined systems, we show that solutions without linear
counterpart do exist in presence of a multi-well external potential. These
solutions, which in the limit of strong nonlinearity have the form of chains of
dark or bright solitons located near the extrema of the potential, represent
macroscopically excited states of a Bose-Einstein condensate and are in
principle experimentally observable.
