Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909306281000960 |
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| author | Maia, Lamiae Khattabi, Noha El Frigon, Marlène |
| author_facet | Maia, Lamiae Khattabi, Noha El Frigon, Marlène |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems Maia, Lamiae Khattabi, Noha El Frigon, Marlène Classical Analysis and ODEs Dynamical Systems 34A06 (Primary) 34D20, 34A34, 34B60 (Secondary) 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. |
| title | Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems |
| topic | Classical Analysis and ODEs Dynamical Systems 34A06 (Primary) 34D20, 34A34, 34B60 (Secondary) |
| url | https://arxiv.org/abs/2409.03408 |