  Through a suitable expansion of the Gross-Pitaevskii equation near the
classical turning point, we obtain an explicit solution for the order parameter
at the boundary of a trapped Bose gas interacting with repulsive forces. The
kinetic energy of the system, in terms of the classical radius $R$ and of the
harmonic oscillator length $a_{_{HO}}$, follows the law $E_{kin}/N \propto
R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, approaching, for large $R$, the
results obtained by solving numerically the Gross-Pitaevskii equation. The
occurrence of a Josephson-type current in the presence of a double trap
potential is finally discussed.
