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Based on Guo-Krasnoselskii’s fixed point theorem, the existence of positive solutions for a class of nonlinear algebraic systems of the form x=GFx is studied firstly, where G is a positive n×n square matrix, x=col⁡(x1,x2,…,xn), and F(x)=col⁡(f(x1),f(x2),…,f(xn)), 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 Rn. 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.

Existence of Positive Solutions for a Class of Nonlinear Algebraic Systems