  We consider a model of N two-dimensional bosons in a harmonic trap with
translational and rotational invariant, weak two-particle interaction. We
present in configuration space a systematical recursive method for constructing
all wave functions with angular momentum L and corresponding energies and apply
it to L\leq 6 for all N. The lower and the upper bounds for interaction energy
are estimated. We analitically confirm the conjecture of Smith et al. that
elementary symmetric polynomial is the ground state for repulsive delta
interaction, for all N\geq L up to L\leq 6. Additionally, we find that there
exist vanishing-energy solutions for L\geq N(N-1), signalizing the exclusive
statistics. Finally, we consider briefly the case of attractive power-like
potential r^k, k>-2, and prove that the lowest-energy state is still the one in
which all angular momentum is absorbed by the center-of-mass motion.
