  We show that the Gross-Pitaevskii equation with cubic nonlinearity, as a
model to describe the one dimensional Bose-Einstein condensates loaded into a
harmonically confined optical lattice, presents a set of ground states which is
orbitally stable for any value of the self-interaction (attractive and
repulsive) parameter and laser intensity. We also derive a new formalism which
gives explicit expressions for the minimum energy and the associated chemical
potential. Based on these formulas, we generalize the variational method to
obtain approximate solutions, at any order of approximation, for the energy,
the chemical potential and the ground state.
