  We obtain a continuous family of nontrivial domains $\Omega_s\subset
\mathbb{R}^N$ ($N=2,3$ or $4$), bifurcating from a small ball, such that the
problem \begin{equation} -\Delta u=u-\left(u^+\right)^3\,\,
\text{in}\,\,\Omega_s, \,\, u=0,\,\,\partial_\nu
u=\text{const}\,\,\text{on}\,\,\partial\Omega_s \nonumber \end{equation} has a
sign-changing bounded solution. Compared with the recent result obtained by
Ruiz, here we obtain a family domains $\Omega_s$ by using Crandall-Rabinowitz
bifurcation theorem instead of a sequence of domains.
