Author:
Jia Keke,Hong Shihuang,Cao Xiaoyu,Yue Jieqing
Abstract
AbstractWe first present a new definition for some form of exponential stability of solutions, including H-exponential stability, H-exponentially asymptotic stability, H-uniformly exponential stability, and H-uniformly exponentially asymptotic stability for a class of set dynamic equations on time scales. Employing Lyapunov-like functions on time scales, we provide the sufficient conditions for the exponential stability of the trivial solution for such set dynamic equations.
Funder
The National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference36 articles.
1. Lakshmikantham, V., Leela, S., Vastla, A.S.: Interconnection between set and fuzzy differential equations. Nonlinear Anal. TMA 54(2), 351–360 (2003)
2. Bhaskar, T.G., Lakshmikantham, V.: Set differential equations and flow invariance. Appl. Anal. 82(4), 357–368 (2003)
3. Bhaskar, T.G., Lakshmikantham, V.: Lyapunov stability for set differential equations. Dyn. Syst. Appl. 13, 1–10 (2004)
4. Bhaskar, T.G., Shaw, M.: Stability results for set difference equations. Dyn. Syst. Appl. 13(3–4), 479–485 (2004)
5. Bhaskar, T.G., Devi, J.V.: Stability criteria for set differential equations. Math. Comput. Model. 41(11–12), 1371–1378 (2005)