Analysis of Functional Integral Equations, Generalized Ordinary Differential Equat...
Continuation of abstract Lyapunov graphs and the maximal number of Betti number va...
| Full text | |
| Author(s): |
Bonotto, Everaldo M.
;
Bortolan, Matheus C.
;
Pereira, Fabiano
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 384, p. 47-pg., 2023-12-18. |
| Abstract | |
In this paper, we present a comprehensive theory of generalized gradient and dynamically gradient impulsive semigroups. Our work establishes the equivalence of these classes, relative to a separated family of isolated invariant sets, similar to the non-impulsive case. However, the presence of impulses poses certain challenges, which we overcome by considering a slightly modified notion of attraction. Additionally, we provide an illustration of the theory by demonstrating that a reaction-diffusion equation-driven impulsive semigroup possesses a Lyapunov function. (c) 2023 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 20/14075-6 - Dynamical systems and their attractors under perturbations |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |