Systems of nonlinear algebraic equations with positive solutions. 2017

Anca Ciurte, and Sergiu Nedevschi, and Ioan Rasa
Department of Computer Science, Technical University of Cluj Napoca, 26-28th G. Baritiu Street, Cluj-Napoca, 400027 Romania.

We are concerned with the positive solutions of an algebraic system depending on a parameter [Formula: see text] and arising in economics. For [Formula: see text] we prove that the system has at least a solution. For [Formula: see text] 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.

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