The behavior of solutions of singular initial value problems is studie
d for a second order ordinary differential equation. The main purpose
of this paper is to obtain sharp sufficient conditions so that any sol
ution has a finite number of zeros or infinitely many zeros. We treat
them systematically and generalize previous results by using the Pohoz
aev identity. As an application, we investigate the number of zeros of
radially symmetric solutions to generalized Laplace equations.