Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems

Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems

In this article, we present Lyapunov-type results to study the stability of an equilibrium 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 stability (resp. uniform...

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Bibliographic Details
Main Authors: Lamiae Maia, Noha El Khattabi, Marlene Frigon
Format: Article
Language:English
Published: University of Szeged 2025-05-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Subjects:
stieltjes differential equations
lyapunov stability
lyapunov function
stable equilibrium
asymptotic stability
dynamical system
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=11407
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Summary:In this article, we present Lyapunov-type results to study the stability of an equilibrium 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 stability (resp. uniform stability) and asymptotic stability (resp. asymptotic uniform stability). Finally, we present examples and real-life applications to study asymptotic stability of equilibria in two population dynamics models.
ISSN:1417-3875

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