On the uniform asymptotic stability to certain first order neutral differential equations

 

Cemil Tunc¹

¹Department of Mathematics, Faculty of Science, Yüzüncü Yıl University, 65080, Van, Turkey cemtunc@yahoo.com

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ABSTRACT
In this paper, the uniform asymptotic stability of the zero solution of a kind of neutral differential equations is discussed. Based on the Lyapunov functional approach, a new stability criterion is derived, which is delay dependent on two positive constants. The result to be obtained here extends and generalizes the existing ones in the literature.

Keywords and Phrases: Neutral differential equation; first order, uniform asymptotic stability; Lyapunov functional.

2010 AMS Mathematics Subject Classification: 34K20, 34K40.

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RESUMEN
En este artículo se discute la estabilidad asintótica uniforme de la solución cero de un tipo de ecuaciones diferenciales neutrales. Basados en la técnica de funcional de Lyapunov, se deriva un nuevo criterio de estabilidad, el cual es dependiente de atrasos basados en dos constantes positivas. El resultado que se obtiene extiende y generaliza los encontrados en la literatura.

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References

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Received: December 2012. Revised: May 2013.