含Causal算子的脉冲微分方程的两度量稳定性
Stability for Impulsive Differential Systems with Causal Operators in Terms of Two Measures
DOI: 10.12677/PM.2022.129161, PDF,    科研立项经费支持
作者: 王文丽：河北大学管理学院，河北 保定；田淑环：保定学院数学与计算机系，河北 保定
关键词: Causal算子；脉冲微分系统；两度量稳定性；Causal Operators； Impulsive Differential Systems； In Terms of Two Measures
摘要: 脉冲微分方程理论是微分方程理论的一个重要分支，相对于微分方程理论而言，脉冲微分方程理论有着更为广泛的应用，因此许多研究者对此产生了浓厚的兴趣，其中脉冲微分方程的稳定性是其理论中的重要分支。本文引入函数上拟单调的概念，并建立了新的比较原理，运用这个比较原理和李雅普诺夫函数，从而得到了含有causal算子的脉冲微分系统的两度量稳定性的一些判据，从而丰富了脉冲微分系统的研究结果。
Abstract: Impulse differential equation theory is an important branch of differential equation theory. Compared with differential equation theory, impulse differential equation theory has a wider range of applications, among which the stability of impulse differential equation is an important branch of its theory, so many researchers have a keen interest in it. In this paper, a new concept of quasi-monotone function is introduced, and a new comparison principle is also established. By using this principle and Lyapunov functions, some criteria about stability for impulsive differential equations with causal operators in terms of two measures are obtained. This enriches the research results of impulsive differential systems.
文章引用：王文丽, 田淑环. 含Causal算子的脉冲微分方程的两度量稳定性[J]. 理论数学, 2022, 12(9): 1481-1486. https://doi.org/10.12677/PM.2022.129161

参考文献

[1] 廖晓昕. 动力系统的稳定性理论和应用[M]. 北京: 国防工业出版社, 2000: 4, 67-70.
[2] 彭临平. 具有扰动的脉冲微分系统的稳定性[J]. 山西大学学报(自然科学版), 1994, 17(1): 5-8.
[3] Lakshmikantham, V. and Liu, X.Z. (1998) Stability for Impulsive Differential Systems in Terms of Two Measures, Applied Mathematics and Computation, 29, 89-98.
[4] 鲍俊艳, 高春霞, 周彩丽. 脉冲微分方程的两度量实用稳定性[J]. 数学的实践与认识, 2008, 38(9): 166-171.
[5] 田淑环. 时间尺度上脉冲微分系统的两度量稳定性[J]. 保定学院学报, 2011, 24(3): 12-14.
[6] Liu, C., Liu, X., Yang, Z., Yang, H. and Huang, J. (2022) New Stability Results of Generalized Impulsive Functional Dif-ferential Equations. Science China. Information Sciences, 65, 244-246. [Google Scholar] [CrossRef] 
[7] Bao, J.Y., Wang, P.G. and Li, Y. (2020) Practical Stability and Integral Stability for Singular Differential Systems with Maxima. Mathematical Problems in Engineering, 2020, Article ID 4792183. [Google Scholar] [CrossRef] 
[8] Wang, P.G. and Bao, J.Y. (2020) Asymptotic Stability of Neutral Set-Valued Functional Differential Equation by Fixed Point Method. Discrete Dynamics in Nature and Society, 2020, Article ID 6569308. [Google Scholar] [CrossRef] 
[9] Mchiri, L., Mohsen, B. and Caraballo, T. (2022) η-Stability of Hybrid Neutral Stochastic Differential Equations with Infinite Delay. International Journal of Robust and Nonlinear Control, 32, 1973-1989. [Google Scholar] [CrossRef] 
[10] Lakshmikantham, V., Leela, S., Drici, Z. and McRae, F.A. (2009) Theory of Causal Differential Equations. World Scientific, Singapore.

为你推荐