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Exponential stability of nonlinear impulsive neutral integro-differential equations. (English) Zbl 1155.34354

Summary: A nonlinear impulsive neutral integro-differential equation with time-varying delays is considered. By establishing a singular impulsive delay integro-differential inequality and transforming the \(n\)-dimensional impulsive neutral integro-differential equation into a \(2n\)-dimensional singular impulsive delay integro-differential equation, some sufficient conditions ensuring the global exponential stability in \(PC^{1}\) of the zero solution of an impulsive neutral integro-differential equation are obtained. The results extend and improve the earlier publications. An example is also discussed to illustrate the efficiency of the obtained results.

MSC:

34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses
45J05 Integro-ordinary differential equations
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