测度泛函微分方程的Lyapunov稳定性
Lyapunov Stability of Measure Functional Differential Equations
摘要: 利用广义常微分方程与测度泛函微分方程的等价关系，定义了测度泛函微分方程的稳定，渐进稳定及指数稳定的概念，并借助此概念及Lyapunov泛函证明了测度泛函微分方程稳定性的相关定理。
Abstract: By using the equivalent relation between generalized ordinary differential equations and measure functional differential equations, we define notions of the stability, asymptotic and exponential stability of measure function differential equations. Furthermore, according to the notions and Lyapunov function, the theorems of Measure functional differential equations are established.
文章引用：周云菲, 李宝麟. 测度泛函微分方程的Lyapunov稳定性[J]. 理论数学, 2022, 12(1): 197-208. https://doi.org/10.12677/PM.2022.121024

参考文献

[1] Oliva, F. and Vorel, Z. (1966) Functional Equations and Generalized Ordinary Differential Equations. Boletín de la Sociedad Matemática Mexicana, 11, 40-46.
[2] Federson, M., Mesquita, J.G. and Slavík, A. (2012) Measure Func-tional Differential Equations and Functional Dynamic Equations on Time Scales. Journal of Differential Equations, 252, 3816-3847. [Google Scholar] [CrossRef] 
[3] Das, P.C. and Sharma, R.R. (1972) Existence and Stability of Measure Differential Equations. Czechoslovak Mathematical Journal, 22, 145-158. [Google Scholar] [CrossRef] 
[4] Afonso, S.M. and Da Silva, M.R. (2019) Lipschitz Stability of Generalized Ordinary Differential Equations and Impulsive Retarded Differential Equations. Electronic Journal of Qualitative Theory of Differential Equations, 2019, 1-18. [Google Scholar] [CrossRef] 
[5] Federson, M., Mesquita, J.G. and Toon, E. (2015) Lyapunov The-orems for Measure Functional Differential Equations via Kurzweil Equations. Mathematische Nachrichten, 288, 1487-1511. [Google Scholar] [CrossRef] 
[6] da Silva, F.A., Federson, M., Grau, R. and Toon, E. (2021) Converse Lyapunnov Theorems for Measure Functional Differential Equations. Journal of Differential Equations, 286, 1-46. [Google Scholar] [CrossRef] 
[7] Federson, M., Grau, R. and Mesquita, J.G. (2019) Prolongation of Solutions of Measure Differential Equations and Dynamic Equations on Time Scales. Mathematische Nachrichten, 292, 22-55. [Google Scholar] [CrossRef] 
[8] Federson, M., Grau, R., Mesquita, J.G. and Toon, E. (2019) Lyapunov Stability for Measure Differential Equations and Dynamic Equations on Time Scales. Journal of Differential Equations, 267, 4192-4223. [Google Scholar] [CrossRef] 
[9] Gallegos, C.A., Grau, R. and Mesquita, J.G. (2021) Stability, As-ymptotic and Exponential Stability for Various Types of Equations with Discountinuous Solutions via Lyapunov Functionals. Journal of Differential Equations, 299, 256-283. [Google Scholar] [CrossRef] 

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