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Stability of functional differential equations with impulses. (English) Zbl 1118.34079

The authors establish some comparison theorems for functional differential equations (FDE) with impulses using several Lyapunov-Razumikhin. The comparison theorems are employed to develop sufficient conditions for stability theorems for FDE. An example is given to illustrate the usefulness and advantages of the results.

MSC:

34K45 Functional-differential equations with impulses
34K20 Stability theory of functional-differential equations
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References:

[1] Xing, Y. P.; Han, M. A., A new approach to stability of impulsive functional differential equations, Appl. Math. Comput., 151, 835-847 (2004) · Zbl 1057.34103
[2] Yan, J. R.; Shen, J. H., Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions, Nonlinear Anal., 37, 245-255 (1999) · Zbl 0951.34049
[3] Zhang, S. N., A new approach to stability theory of functional differential equations, Ann. Differential Equations, 11, 4, 495-503 (1995) · Zbl 0841.34079
[4] Ballinger, G.; Lui, X., Existence, uniqueness and boundedness results for impulsive delay differential equations, Appl. Anal., 74, 71-93 (2000) · Zbl 1031.34081
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