In the first part of the talk I will review some of the results known for weakly interacting 
bosons in box shaped and harmonic traps. Many results can be concluded from heuristic 
and dimensional arguments [1]. In the second part this approach will be extended to 
interacting bosons in a potential consisting of a superposition of a harmonic and a 
random potential. New results for the size, shape and excitation energy of the condensate 
as a function of the disorder strength and interaction are found using a semi-quantitative 
analysis. For positive scattering length and sufficiently strong disorder the condensate 
decays into fragments each of the size of the Larkin length. This state is stable over 
a large range of particle numbers. For negative scattering length a condensate of size 
of the Larkin length may exist as a metastable state. These findings are generalized to 
anisotropic traps[2]. 

[1] T. Nattermann, Am. J. Phys. 73, 349(2005), 75, 938(2007). 
[2] T. Nattermann and V.L. Pokrovsky, Bose-Einstein Condensates 
    in Strongly Disordered Taps arXiv: 0707.4444