Lyapunov functions for dynamically gradient impulsive systems

被引：1

作者：

Bonotto, Everaldo M. ^{[1
]}

Bortolan, Matheus C. ^{[2
]}

Pereira, Fabiano ^{[3
]}

机构：

[1] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, Campus Sao Carlos 668, BR-13560970 Sao Carlos, SP, Brazil

[2] Univ Fed Santa Catarina, Dept Matemat, Campus Florianopolis, Florianopolis, SC, Brazil

[3] Univ Fed Fronteira, Campus Cerro Largo, Cerro Largo, RS, Brazil

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 384卷

基金：

巴西圣保罗研究基金会;

关键词：

Impulsive semigroups; Gradient impulsive semigroups; Dynamically gradient impulsive semigroups; Isolated invariant sets; Lyapunov function; PULLBACK ATTRACTORS; GLOBAL ATTRACTORS; SEMICONTINUITY;

D O I：

10.1016/j.jde.2023.12.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：279 / 325

页数：47

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