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Razumikhin method for impulsive functional differential equations of neutral type. (English) Zbl 1373.34109

Summary: Although the well-known Razumikhin method has been well developed for the stability of functional differential equations with or without impulses and it is very useful in applications, so far there is almost no result of Razumikhin type on stability of impulsive functional differential equations of neutral type. The purpose of this paper is to close this gap and establish some Razumikhin-based stability results for impulsive functional differential equations of neutral type. A kind of auxiliary function \(N(t)\) that has great randomicity is introduced to Razumikhin condition. Some examples are given to show the effectiveness and advantages of the developed method.

MSC:

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