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Mathematical Problems in Engineering
Volume 2016, Article ID 6120169, 7 pages
Research Article

Existence of Positive Solutions for a Class of Nonlinear Algebraic Systems

1School of Science, Tianjin University of Commerce, Tianjin 300134, China
2Department of Mathematics, Department of Computing and Information Systems, Trent University, Peterborough, ON, Canada K9J 7B8

Received 28 October 2015; Revised 29 December 2015; Accepted 30 December 2015

Academic Editor: Evangelos J. Sapountzakis

Copyright © 2016 Yongqiang Du et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on Guo-Krasnoselskii’s fixed point theorem, the existence of positive solutions for a class of nonlinear algebraic systems of the form is studied firstly, where is a positive square matrix, , and , where, is not required to be satisfied sublinear or superlinear at zero point and infinite point. In addition, a new cone is constructed in . Secondly, the obtained results can be extended to some more general nonlinear algebraic systems, where the coefficient matrix and the nonlinear term are depended on the variable . Corresponding examples are given to illustrate these results.