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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Exponentially Dichotomous Linear systems of Differential Equations with Piecewise Constant Argument

Discontinuity, Nonlinearity, and Complexity 1(4) (2012) 337--352 | DOI:10.5890/DNC.2012.09.001

M. Akhmet

Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey

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Abstract

We consider differential equations with piecewise constant argument of generalized type. It is the first time, an attention is given to the exponential dichotomy of linear systems. Bounded, almost periodic and periodic solutions and their stability are discussed. The study is made in such a way that further construction of the theory will follow for ordinary differential equations. The results are illustrated by examples.

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