Existence of positive solutions for a class of nonlinear algebraic systems (Q1793400)

Summary: Based on Guo-Krasnoselskii's fixed point theorem, the existence of positive solutions for a class of nonlinear algebraic systems of the form \(x = G F \left(x\right)\) is studied firstly, where \(G\) is a positive \(n \times n\) square matrix, \(x = \operatorname{col}(x_1, x_2, \ldots, x_n)\), and \(F(x) = \operatorname{col}(f(x_1), f(x_2), \ldots, f(x_n))\), where, \(F(x)\) is not required to be satisfied sublinear or superlinear at zero point and infinite point. In addition, a new cone is constructed in \(R^n\). Secondly, the obtained results can be extended to some more general nonlinear algebraic systems, where the coefficient matrix \(G\) and the nonlinear term are depended on the variable \(x\). Corresponding examples are given to illustrate these results.