Systems of nonlinear algebraic equations with positive solutions

被引：5

作者：

Ciurte, Anca ^{[1
]}

Nedevschi, Sergiu ^{[1
]}

Rasa, Ioan ^{[2
]}

机构：

[1] Tech Univ Cluj Napoca, Dept Comp Sci, 26-28th G Baritiu St, Cluj Napoca 400027, Romania

[2] Tech Univ Cluj Napoca, Dept Math, 26-28th G Baritiu St, Cluj Napoca 400027, Romania

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年

关键词：

nonlinear algebraic system; positive solution; existence; uniqueness; EXISTENCE;

D O I：

10.1186/s13660-017-1454-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the positive solutions of an algebraic system depending on a parameter alpha > 0 and arising in economics. For alpha > 1 we prove that the system has at least a solution. For 0 < alpha < 1 we give three proofs of the existence and a proof of the uniqueness of the solution. Brouwer's theorem and inequalities involving convex functions are essential tools in our proofs.

引用

页数：6

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