CPAA
Quasilinear retarded differential equations with functional dependence on piecewise constant argument
Marat Akhmet
Communications on Pure & Applied Analysis 2014, 13(2): 929-947 doi: 10.3934/cpaa.2014.13.929
We introduce a new class of differential equations, retarded differential equations with functional dependence on piecewise constant argument, $RFDEPCA$ and focus on quasilinear systems. Formulation of the initial value problem, bounded solutions, periodic and almost periodic solutions, their stability are under investigation. Illustrating examples are provided.
keywords: Bohr almost periodic solutions periodic solutions exponential stability. Retarded differential equations alternate constancy of argument functional dependence on piecewise constant argument
DCDS
Lyapunov-Razumikhin method for differential equations with piecewise constant argument
Marat Akhmet Duygu Aruğaslan
Discrete & Continuous Dynamical Systems - A 2009, 25(2): 457-466 doi: 10.3934/dcds.2009.25.457
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

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