Integral equation for inhomogeneous condensed bosons generalizing the   Gross-Pitaevskii differential equation
  We give here the derivation of a Gross-Pitaevskii--type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91 (2003) 030401]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided. 
G. G. N. Angilella, N. H. March, R. Pucci