  This work deals with the system $(-\Delta)^m u= a(x) v^p$, $(-\Delta)^m
v=b(x) u^q$ with Dirichlet boundary condition in a domain $\Omega\subset\RR^n$,
where $\Omega$ is a ball if $n\ge 3$ or a smooth perturbation of a ball when
$n=2$.
  We prove that, under appropriate conditions on the parameters
($a,b,p,q,m,n$), any non-negative solution $(u,v)$ of the system is bounded by
a constant independent of $(u,v)$. Moreover, we prove that the conditions are
sharp in the sense that, up to some border case, the relation on the parameters
are also necessary.
  The case $m=1$ was considered by Souplet in \cite{PS}. Our paper generalize
to $m\ge 1$ the results of that paper.
