We study the problem of existence and nonexistence of
positive, spherically symmetric solutions of a quasilinear elliptic
system involving p-Laplacians, with the natural growth in the gradient on the right-hand sfide. The existence proof is constructive,
with solutions possessing explicit integral representation. We also
obtain various qualitative results. The elliptic system is studied
by relating it to the corresponding system of singular ODE's of
the first order.
