A semilinear system with positivity conditions

• Carlos Conca ^[1] ; Raúl Gormaz ^[1] ; Jorge San Martin ^[1]
  1. [1] Universidad de Chile
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 76, Nº. 1, 2019, págs. 143-152
• Idioma: inglés
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• Resumen

  • This paper studies a semi-linear system of equations in RN, 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×N. The proof of the results is based on a monotony method with respect to the usual lexicographic order in RN.