LYAPUNOV-RAZUMIKHIN METHOD FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT


AKHMET M. , Arugaslan D.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol.25, no.2, pp.457-466, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.3934/dcds.2009.25.457
  • Title of Journal : DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
  • Page Numbers: pp.457-466
  • Keywords: Differential equations with piecewise constant argument of generalized type, Lyapunov's second method, Razumikhin technique, logistic equation, ALMOST-PERIODIC SOLUTIONS, GENERALIZED TYPE, GLOBAL STABILITY, DELAYS, PERSISTENCE, SYSTEMS, MODEL

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.