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On the stability of impulsive functional differential equations with infinite delays
Author(s) -
Li Xiaodi,
Caraballo T.,
Rakkiyappan R.,
Han Xiuping
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3303
Subject(s) - mathematics , stability (learning theory) , exponential stability , differential equation , lyapunov function , mathematical analysis , nonlinear system , computer science , physics , quantum mechanics , machine learning
In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results. Copyright © 2014 John Wiley & Sons, Ltd.