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...

Full description

Saved in:
Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2025; no. 19; pp. 1 - 37
Main Authors Maia, Lamiae, El Khattabi, Noha, Frigon, Marlene
Format Journal Article
LanguageEnglish
Published University of Szeged 01.01.2025
Subjects
asymptotic stability
dynamical system
lyapunov function
lyapunov stability
stable equilibrium
stieltjes differential equations
Online AccessGet full text

Cover

More Information
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
1417-3875
DOI:10.14232/ejqtde.2025.1.19