On positive radial entire solutions of second-order quasilinear elliptic systems

We study positive radial entire solutions of second-order quasilinear elliptic systems of the form Δpu = f |x|,u, v , Δq v = g |x|,u, v , x∈ RN. (∗) Sufficient and/or necessary conditions of f and g are obtained for (∗) to have positive radial entire solutions with prescribed asymptotic behavior at infinity. We first study the upper and lower estimates for the nonlinear integral operator, which is “inverse” of one-dimensional polar form of the N-dimensional m-Laplace operator.  2003 Elsevier Inc. All rights reserved.