Systems of nonlinear algebraic equations with positive solutions
Anca Ciurte1, Sergiu Nedevschi1, Ioan Rasa2
1Department of Computer Science, Technical University of Cluj Napoca, 26-28th G. Baritiu Street, Cluj-Napoca, 400027 Romania.
Journal of Inequalities and Applications
|August 22, 2017
Summary
This study proves the existence of positive solutions for an economic algebraic system. For specific parameter values, it demonstrates both the existence and uniqueness of these solutions.
Area of Science:
- Economic modeling
- Mathematical economics
- Applied mathematics
Background:
- An algebraic system arises in economic modeling.
- The system's solutions depend on a parameter, denoted as [Formula: see text].
Purpose of the Study:
- To investigate the existence of positive solutions for the algebraic system.
- To analyze the solution behavior for different parameter values of [Formula: see text].
Main Methods:
- The study employs Brouwer's theorem.
- Inequalities involving convex functions are utilized as essential tools.
Main Results:
- For a specific parameter range ([Formula: see text]), the existence of at least one positive solution is proven.
- For another parameter range ([Formula: see text]), three proofs establish the existence of a solution.
- For [Formula: see text], a single proof confirms the uniqueness of the solution.
Conclusions:
- The algebraic system, relevant to economics, possesses positive solutions under specific parameter conditions.
- The proofs leverage established mathematical theorems and inequalities, highlighting the system's well-defined nature.
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