In this article a perturbative solution of the Gross–Pitaevskii(GP) equation in the D-dimensional space RD with a general continuous non-negative external potential is studied. The solution describes the condensate wave-function of a gas containing N Bose particles. A criteria for the validity of the perturbative solution is developed. Furthermore expressions for the particle density, the chemical potential, the internal energy and the mean-square radius of the condensate are derived corrected to first order in the coupling constant. The scheme is then applied to obtain the solution of the GP equation in D=1,2,3 for external harmonic potentials, and the results are compared with the numerical solutions. It is shown, in each case, that if N exceeds a certain value the perturbative solution breaks down.