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July  2009, 25(2): 457-466. doi: 10.3934/dcds.2009.25.457

Lyapunov-Razumikhin method for differential equations with piecewise constant argument

Marat Akhmet 1, and  Duygu Aruğaslan 1,

1. 

Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey, Turkey

Received  June 2008 Revised  December 2008 Published  June 2009

At the first time, Razumikhin technique is applied for differential equations with piecewise constant argument of generalized type [1, 2]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.
Keywords: Lyapunov's second method, Razumikhin technique, logistic equation., Differential equations with piecewise constant argument of generalized type.
Mathematics Subject Classification: 34A36, 34D20, 34K20, 34K60, 92D2.
Citation: Marat Akhmet, Duygu Aruğaslan. Lyapunov-Razumikhin method for differential equations with piecewise constant argument. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 457-466. doi: 10.3934/dcds.2009.25.457
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