Author:
Jia Yanping,Gao Ying,Feng Wenying,Zhang Guang
Abstract
AbstractExistence of positive solutions for the nonlinear algebraic system$x=\lambda GF ( x ) $x=λGF(x)has been extensively studied when the$n\times n$n×ncoefficient matrixGis positive or nonnegative. However, to the best of our knowledge, few results have been obtained when the coefficient matrix changes sign. In this case, some commonly applied analysis methods such as the cone theory, the Krein–Rutman theorem, the monotone iterative techniques, and so on cannot be directly applied. In this note, we prove the existence of positive solutions for the above nonlinear algebraic system with sign-changing coefficient matrix taking the advantages of the classical Brouwer fixed point theorem combined with a decomposition condition on the coefficient matrix. We provide an example in solving a second-order difference equation with periodic boundary conditions to illustrate the applications of the results.
Funder
the Natural Sciences and Engineering Research Council of Canadasen Toimikunta
Natural Science Foundation of Tianjin
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Cited by
2 articles.
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