The behavior of a trapped atomic gas undergoing a Bose-Einstein conden
sation is strongly influenced by the attractive interaction between pa
rticles. The role played by such an interaction is analyzed by means o
f a variation method. The critical number of atoms for a metastable st
ate to exist is determined, The aspect ratio of condensed bosons in an
anisotropic trap, the loss rate of atoms, and the excitation spectrum
are studied. The vortex state is discussed.