  In this work we study the nonnegative solutions of the elliptic system \Delta
u=|x|^{a}v^{\delta}, \Delta v=|x|^{b}u^{\mu} in the superlinear case \mu
\delta>1, which blow up near the boundary of a domain of R^{N}, or at one
isolated point. In the radial case we give the precise behavior of the large
solutions near the boundary in any dimension N. We also show the existence of
infinitely many solutions blowing up at 0. Furthermore, we show that there
exists a global positive solution in R^{N}\{0}, large at 0, and we describe its
behavior. We apply the results to the sign changing solutions of the biharmonic
equation \Delta^2 u=|x|^{b}|u|^{\mu}. Our results are based on a new dynamical
approach of the radial system by means of a quadratic system of order 4,
combined with nonradial upper estimates.
