Summary: The physics of Bose-Einstein condensation can be described by the nonlinear Gross-Pitaevskii equation. We study the ground state energy of the condensates induced by an external perturbation at the trapping frequency applied. This equation and some of the physics behind it is investigated here. It is put in a form so that the nonlinear term in the equation is treated as a perturbation. Using first-order perturbation theory, corrections to the unperturbed energy are calculated in one dimension, three dimensions and the spherically symmetric case.