In this paper by an application of Krasnoselskii’s fixed point theorem, we establish the existence of infinitely many positive radial solutions to the iterative system of nonlinear elliptic equations of the form Δvj+(N-2)2r02N-2|x|2N-2vj+Q(|x|)gj(vj+1)=0,x∈Ω,vj|∂Ω=0,lim|x|→∞vj(x)=0,\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\begin{aligned} \begin{aligned}&\varDelta { v_{\mathtt {j}}}+\frac{(N-2)^2r_0^{2N-2}}{\vert \mathtt {x}\vert ^{2N-2}}v_\mathtt {j}+\mathtt {Q}(\vert \mathtt {x}\vert )\mathtt {g}_{\mathtt {j}}( v_{\mathtt {j}+1})=0,~~\mathtt {x}\in \varOmega ,\\&\quad v_{\mathtt {j}}\vert _{\partial \varOmega }=0,~ \lim _{\vert \mathtt {x}\vert \rightarrow \infty }v_{\mathtt {j}}(\mathtt {x})=0, \end{aligned} \end{aligned}$$\end{document}where j∈{1,2,3,…,m},\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathtt {j}\in \{1,2,3,\ldots ,m\},$$\end{document}v1=vm+1,\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$ v_1= v_{m+1},$$\end{document}Δv=div(∇v),\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\varDelta v=\mathtt {div}(\nabla v),$$\end{document}N>2,\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$N>2,$$\end{document}0<r0<π/2,\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$0<r_0<\pi /2,$$\end{document}Ω={v∈RN||v|>r0},\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\varOmega =\{ v\in \mathbb {R}^N|~\vert v\vert >r_0\},$$\end{document}Q=∏i=1nQi,\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathtt {Q}=\prod _{i=1}^{n}\mathtt {Q}_i,$$\end{document} each Qi:(r0,+∞)→(0,+∞)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathtt {Q}_i:(r_0,+\infty )\rightarrow (0,+\infty )$$\end{document} is continuous, rN-1Q\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$r^{N-1}\mathtt {Q}$$\end{document} is integrable, may have singularities, and gj:[0,+∞)→R\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$\mathtt {g}_\mathtt {j}:[0,+\infty )\rightarrow \mathbb {R}$$\end{document} is continuous.
