Unique Solutions to Power-Transformed Affine Systems

2022/12/01 by John Stachurski, Stachurski, John, Ole Wilms +3 · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2212.00275

openalex publication_date 2022/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Systems of the form x = (A x^s)^1/s + b arise in a range of economic, financial and control problems, 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 and complete characterization of existence and uniqueness of positive solutions under conditions on A and b that imply positivity.

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