Stieltjes differential equations with bounded-variation derivators and application to thermal stress in solar panels

TL;DR

This paper extends Stieltjes differential equations to non-monotone derivators, develops new theoretical tools, and applies these to model thermal stress in solar panels, demonstrating practical relevance.

Contribution

It introduces a generalized theory of Stieltjes systems with non-monotone derivators, including new calculus rules and solution concepts.

Findings

Established chain rules and fundamental theorem for non-monotone Stieltjes systems.

Developed a $g$-exponential for explicit linear solutions.

Applied the theory to model thermal stress in solar panels.

Abstract

In this work we extend the theory of Stieltjes systems beyond the monotone case, establishing new chain rules, generalized versions of the Fundamental Theorem of Calculus, compactness tools for Peano-type results, and a $g$-exponential for explicit linear solutions. Continuity notions relative to vector-valued derivators further allow us to study everywhere differentiable solutions. As an application, we model thermal stress effects on solar panels and battery health, highlighting the practical value of non-monotone derivators.