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

AbstractWe study positive radial entire solutions of second-order quasilinear elliptic systems of the form (∗)Δpu=f|x|,u,v,Δqv=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