SeMA Journal

, Volume 76, Issue 1, pp 143–152 | Cite as

A semilinear system with positivity conditions

  • Carlos Conca
  • Raúl GormazEmail author
  • Jorge San Martin


This paper studies a semi-linear system of equations in \( {\mathbb{R}}^{N} \), which comes from a mathematical model for a new tax system proposed in Chile’s 2014 Tax Reform. The system of equations involves a non negative coefficients matrix and simultaneously relates the unknown vector with its positive part, and hence the nonlinear nature of the problem. In addition to find appropriate conditions for the existence and the uniqueness of a solution, in this paper an algorithm is proposed to obtain it by solving at most \( N \) linear systems of size \( N \times N \). The proof of the results is based on a monotony method with respect to the usual lexicographic order in \( {\mathbb{R}}^{N} \).


Semilinear system of equations Positivity condition Order method Taxation system 

Mathematics Subject Classification

15A45 15B48 91B64 



The authors received partial support from PFBasal-01 (CeBiB) and AFB170001 (CMM) projects.


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Copyright information

© Sociedad Española de Matemática Aplicada 2018

Authors and Affiliations

  1. 1.Mathematical Engineering Department, Center for Mathematical Modeling-UMI 2807 CNRS-Chile and Center for Biotechnology and BioengineeringUniversidad de ChileSantiagoChile

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