  We discuss the effects of quenched disorder in a dilute Bose-Einstein
condensate confined in a hard walls trap. Starting from the disordered
Gross-Pitaevskii functional, we obtain a representation for the quenched free
energy as a series of integer moments of the partition function. Positive and
negative disorder-dependent effective coupling constants appear in the integer
moments. Going beyond the mean-field approximation, we compute the static
two-point correlation functions at first-order in the positive effective
coupling constants. We obtain the combined contributions of effects due to
boundary conditions and disorder in this weakly disordered condensate. The
ground state renormalized density profile of the condensate is presented. We
also discuss the appearance of metastable and true ground states for strong
disorder, when the effective coupling constants become negative.
