arXiv subjects

Lamiae Maia

Publications and source records attributed to Lamiae Maia.

3 recordsLinked to original sources

arXiv2025

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

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.

math.CA↗

arXiv2025

The Fundamental Theorem of Calculus for Lebesgue-Stieltjes integrals involving non-monotonic derivators

In this work, we extend the concept of the Stieltjes derivative to encompass left-continuous derivators with bounded variation, thereby relaxing the monotonicity constraint. This generalization necessitates a refined definition of the Stieltjes derivative applicable across the entire domain, accommodating derivators that may change sign. We establish a generalized Fundamental Theorem of Calculus for the Lebesgue-Stieltjes integral in this broader context, presenting both "almost-everywhere" and "everywhere" versions. The latter requires a specific condition relating the derivator to its variation function, which we prove to be optimal through a density theorem. Our framework bridges the gap between Stieltjes differential equations and measure differential equations, offering a tool for modeling complex systems with non-monotonic dynamics.

math.CA↗

arXiv2024

Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems

In this article, we introduce Lyapunov-type results to investigate the stability of the trivial solution of a Stieltjes dynamical system. We utilize prolongation results to establish the global existence of the maximal solution. Using Lyapunov's second method, we establish results of (uniform) stability and (uniform) asymptotic stability by employing a Lyapunov function. Additionally, we present examples and real-life applications to study asymptotic stability of equilibria in two population dynamics models.

math.CA↗