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Consider the problem \begin{eqnarray*} -\Delta u &=& v^{\frac 2{N-2}},\quadv>0\quad {in}\quad \Omega, -\Delta v &=& u^{p},\:\:\:\quad u>0\quad {in}\quad\Omega, u&=&v\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where$\Omega$ is a bounded convex domain in $\R^N,$ $N>2,$ with smooth boundary$\partial \Omega.$ We study the asymptotic behaviour of the least energysolutions of this system as $p\to \infty.$ We show that the solution remainbounded for $p$ large and have one or two peaks away form the boundary. Whenone peak occurs we characterize its location.Comment: 16 pages, submmited for publicatio

Asymptotic Behaviour of a Semilinear Elliptic System with a Large Exponent