  We construct positive solutions of the semilinear elliptic problem $\Delta u+
\lambda u + u^p = 0$ with Dirichet boundary conditions, in a bounded smooth
domain $\Omega \subset \R^N$ $(N\geq 4)$, when the exponent $p$ is
supercritical and close enough to $\frac{N+2}{N-2}$ and the parameter
$\lambda\in\R$ is small enough. As $p\to \frac{N+2}{N-2}$, the solutions have
multiple blow up at finitely many points which are the critical points of a
function whose definition involves Green's function. Our result extends the
result of Del Pino, Dolbeault and Musso \cite{DDM} when $\Omega$ is a ball and
the solutions are radially symmetric.
