Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems
Classical Analysis and ODEs
2024-09-06 v1 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2409.03408,
title = {Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems},
author = {Lamiae Maia and Noha El Khattabi and Marlène Frigon},
journal= {arXiv preprint arXiv:2409.03408},
year = {2024}
}
Comments
37 pages, 10 figures