The improvement of Razumikhin type theorems for impulsive functional differential equations

In this paper, by using Lyapunov functions and Razumikhin techniques, the stability of impulsive functional differential equations is investigated. The obtained results avoid the difficulty of constructing a P function in Razumikhin’s condition and they generalize and improve the existing theorems....

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Bibliographic Details
Published in:Nonlinear analysis 2009-05, Vol.70 (9), p.3104-3109
Main Authors: Liu, Kaien, Yang, Guowei
Format: Article
Language:English
Subjects:
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Functional differential equation
Global analysis, analysis on manifolds
Impulse
Lyapunov function
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Razumikhin technique
Sciences and techniques of general use
Stability
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper, by using Lyapunov functions and Razumikhin techniques, the stability of impulsive functional differential equations is investigated. The obtained results avoid the difficulty of constructing a P function in Razumikhin’s condition and they generalize and improve the existing theorems. An example is given to illustrate the importance of the obtained results.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2008.04.013