Large Solutions of Elliptic Systems of Second Order and Applications to the Biharmonic Equation

In this work we study the nonnogativo solutions of the elliptic system ?u=|x| ?u ?, ?u = |x| in the superlinear case ?? > 1, which blow up near the boundary of a domain of R,? N or at one isolated point. In the radial case wo give the precise behavior of the largo solutions near the boundary in any dimension N. Wo also show the existence of infinitely many solutions blowing up at O. Furthermore, wo show that there exists a global positive solution in R? N {O}, largo at O, and wo describe its behavior. Wo apply the results to the sign changing solutions of the biharmonic equation ? 2u=x bu ?. Our results arc based on a now dynamical approach of the radial system by means of a quadratic system of order 4, introduced in [4], combined with the nonradial upper estimates of [5].