Unique solutions to power-transformed affine systems

Abstract

Systems of the form $x={\left(A{x}^s\right)}^{1/s}+b$ arise in a range of economic and financial applications, where A is a linear operator acting on a space of real-valued functions (or vectors) and s is a nonzero real value. In these applications, attention is focused on positive solutions. We provide a simple characterization of existence and uniqueness of positive solutions when b is positive and A is irreducible.