On stability in terms of two measures for impulsive systems of functional differential equations

Journal of Mathematical Analysis and Applications

Volumn 326, Issue 1, 2007, Pages 252-265

  Liu, Xinzhi ^a   Wang, Qing ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Impulsive functional differential equation; Lyapunov Razumikhin technique; Partial stability; Uniform asymptotical stability

Indexed keywords

EID: 33750623045     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.02.059     Document Type: Article

References (15)

1. Bainov D.D., and Simeonov P.S. Systems with Impulsive Effect: Stability Theory and Applications (1989), Ellis Horwood, Chichester
2. Ballinger G., and Liu X. Existence and uniqueness results for impulsive delay differential equations. Dyn. Contin. Discrete Impuls. Syst. 5 (1999) 579-591
3. Fu X., and Zhang L. On boundedness and stability in terms of two measures for discrete systems of Volterra type. Commun. Appl. Anal. 6 (2002) 61-71
4. Hale J.K., and Lunel S.M.V. Introduction to Functional Differential Equations (1993), Springer, New York
5. Ignatyev A.O. On the partial equiasymptotic stability in functional differential equations. J. Math. Anal. Appl. 268 (2002) 615-628
6. Lakshmikantham V., Bainov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
7. Lakshmikantham V., and Liu X. Stability criteria for impulsive differential equations in terms of two measures. J. Math. Anal. Appl. 137 (1989) 591-604
8. Lakshmikantham V., and Liu X. Stability Analysis in Terms of Two Measures (1993), World Scientific, Singapore
9. Liu X., and Ballinger G. Existence and continuability of solutions for differential equations with delays and state-dependent impulses. Nonlinear Anal. 51 (2002) 633-647
10. Liu X., and Ballinger G. Uniform asymptotic stability of impulsive delay differential equations. Comput. Math. Appl. 41 (2001) 903-915
11. Liu X., and Xu D. Uniform asymptotic stability of abstract functional differential equations. J. Math. Anal. Appl. 216 (1997) 626-643
12. Luo Z., and Shen J. New Razumikhin type theorems for impulsive functional differential equations. Appl. Math. Comput. 125 (2002) 375-386
13. Shen J., and Yan J. Razumikhin type stability theorems for impulsive functional differential equations. Nonlinear Anal. 33 (1998) 519-531
14. Xu D. Uniform asymptotic stability in terms of two measures for functional differential equations. Nonlinear Anal. 27 (1996) 413-427
15. Yuan C. Stability in terms of two measures for stochastic differential equations. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10 (2003) 895-910