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

Abstract

We study positive radial entire solutions of second-order quasilinear elliptic systems of the form (∗) Δ pu=f |x|,u,v ,Δ qv=g |x|,u,v ,x∈ R N. 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.