  For ordinary differential equation, there is a general local existence theory
if $b$ is only supposed to be continuous (Peano's theorem, 1890), even though
uniqueness may fail in this case. However, the perturbed stochastic
differential equation has a unique strong solution when $b$ is assumed to be
continuous and bounded. Moreover, when $% \varepsilon \rightarrow 0^{+},$ the
solutions to the perturbed SDEs converge, in a suitable sense, to the solutions
of the ODE. This phenomenon has been extensively studied for one-dimensional
case in literature. The goal of present paper is to analyze some
multi-dimensional cases. When $b$ has an isolated zero and is non Lipschitz
continuous at zero, the ODE may have infinitely many solutions. Our main result
shows which solutions of the ODE can be the limits of the solutions of the SDEs
(as $\varepsilon \rightarrow 0^{+}$) by stopping time technique which can be
thought of as responses to the questions imposed by Bafico and Baldi (Small
random perturbation of Peano Phenomena, \emph{Stochastics}, 6, 279-292, (1982).
Page 292). The main novelty consists in the treatment of multi-dimensional case
in a simple manner.
