  For a domain $\Omega\subset\dR^N$ we consider the equation $ -\Delta u +
V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and
$p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive
in a region contained in $\Omega$ and negative outside, and such that the sets
$\{Q_n>0\}$ shrink to a point $x_0\in\Omega$ as $n\to\infty$. We show that if
$u_n$ is a nontrivial solution corresponding to $Q_n$, then the sequence
$(u_n)$ concentrates at $x_0$ with respect to the $H^1$ and certain
$L^q$-norms. We also show that if the sets $\{Q_n>0\}$ shrink to two points and
$u_n$ are ground state solutions, then they concentrate at one of these points.
