  We examine the possibility of Bose-Einstein condensation in one-dimensional
interacting Bose gas subjected to confining potentials of the form $V_{\rm
ext}(x)=V_0(|x|/a)^\gamma$, in which $\gamma < 2$, by solving the
Gross-Pitaevskii equation within the semi-classical two-fluid model. The
condensate fraction, chemical potential, ground state energy, and specific heat
of the system are calculated for various values of interaction strengths. Our
results show that a significant fraction of the particles is in the lowest
energy state for finite number of particles at low temperature indicating a
phase transition for weakly interacting systems.
