Positive radial solutions for p-Laplacian systems

The paper deals with the existence of positive radial solutions for the p-Laplacian system div(|∇ ui|p-2∇ ui)  +  fi(u1, ..., un)  =  0, |x|  <  1, ui(x)  =  0, on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|x| = 1, i = 1, \ldots, n, p > 1, x \in {{\mathbb{R}}}^N$$\end{document} . Here fi, i  = 1,...,n, are continuous and nonnegative functions. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf u}= (u_1, \ldots, u_n), \| {\bf u}\| = \sum^n_{i=1}|u_i|, f^i_0 = \lim_{\| u \|\rightarrow 0} \frac{f^i(u)}{\| {\bf u}\| ^{p-1}}, f^i_\infty = \lim_{\| {\bf u}\| \rightarrow \infty} \frac{f^i(u)}{{\|\bf u}\| ^{p-1}}, i = 1, \ldots , n, {\bf f} = (f^1, \ldots , f^n), {\bf f}_0 = \sum^n_{i=1} f^i_0$$\end{document} and f∞  =  ∑ni=1fi∞. We prove that f0  = ∞ and f∞ = 0 (sublinear), guarantee the existence of positive radial solutions for the problem. Our methods employ fixed point theorems in a cone.