  In this paper we study the following problem \begin{equation} \begin{cases}
-\Delta u=f(u)~&\mbox{in}\ \Omega_\varepsilon,\\ u>0~&\mbox{in}\
\Omega_\varepsilon,\\ u=0~&\mbox{on}\ \partial\Omega_\varepsilon, \end{cases}
\end{equation} where $\Omega_\varepsilon=\Omega\backslash B(P,\varepsilon)$,
$\Omega\subset R^N$ with $N\geq 2$ is a smooth bounded domain,
$B(P,\varepsilon)$ is the ball centered at $P$ and radius $\varepsilon>0$ and
$f$ is a smooth nonlinearity.
  By some computations involving the Green function and degree theory, we
compute the number and location of critical points of solutions for small
$\varepsilon>0$.
