  We show the existence of stationary solutions of a 1-D Gross-Pitaevskii
equation in presence of a multi-well external potential that do not reduce to
any of the eigenfunctions of the associated Schroedinger problem. 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.
