Positive Radial Solutions for a Class of Singular p-Laplacian Systems in a Ball

We prove the existence and nonexistence of positive radial solutions for the system -Δpu1=h1(u2)+μ1f1(u2)inB,-Δpu2=h2(u1)+μ2f2(u1)inB,u1=u2=0on∂B,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{\begin{array}{ll} -\Delta_{p}u_{1}=h_{1}(u_{2})+\mu _{1}f_{1}(u_{2}) & \quad \text{in} \, B, \\ -\Delta_{p}u_{2}=h_{2}(u_{1})+\mu _{2}f_{2}(u_{1}) & \quad \text{in}\, B, \\ u_{1}=u_{2}=0 & \quad \text{on} \, \partial B, \end{array}\right.$$\end{document}where p>1,Δpu=div(|∇u|p-2∇u),B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p > 1, \Delta _{p}u = {\rm div}(|\nabla u|^{p-2}\nabla u), \, B}$$\end{document} is the open unit ball inRN,hi,fi:(0,∞)→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{N},h_{i}, f_{i}:(0,\infty) \rightarrow \mathbb{R}}$$\end{document} with fi asymptotically p-linear at ∞, and μi are positive constants, i = 1, 2.