Systems of nonlinear algebraic equations with positive solutions

Abstract

Abstract We are concerned with the positive solutions of an algebraic system depending on a parameter α > 0 $\alpha> 0$ and arising in economics. For α > 1 $\alpha> 1$ we prove that the system has at least a solution. For 0 < α < 1 $0<\alpha<1$ 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.

Keywords

• nonlinear algebraic system
• positive solution
• existence
• uniqueness