Lyapunov-Razumikhin method for differential equations with piecewise constant argument

Marat Akhmet; Duygu Aruğaslan

doi:10.3934/dcds.2009.25.457

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2009, Volume 25, Issue 2: 457-466. Doi: 10.3934/dcds.2009.25.457

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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

Received: May 31, 2008

Revised: November 30, 2008

Published: May 2009

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Abstract

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:

Differential equations with piecewise constant argument of generalized type,
Lyapunov's second method,
Razumikhin technique,
logistic equation.

Mathematics Subject Classification: 34A36, 34D20, 34K20, 34K60, 92D25.

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