Positive solutions of quasilinear elliptic systems with the natural growth in the gradient

Abstract

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.