On the reduction principle for differential equations with piecewise constant argument of generalized type

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2007-12-01

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Akhmet, Marat

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In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA [K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297; J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993]. The Reduction Principle [V.A. Pliss, The reduction principle in the theory of the stability of motion, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1964) 1297-1324 (in Russian); V.A. Pliss, Integral Sets of Periodic Systems of Differential Equations, Nauka, Moskow, 1977 (in Russian)] is proved for EPCAG. The structure of the set of solutions is specified. We establish also the existence of global integral manifolds of quasilinear EPCAG in the so-called critical case and investigate the stability of the zero solution. (c) 2007 Elsevier Inc. All rights reserved.

Subject Keywords

Applied Mathematics, Analysis

URI

https://hdl.handle.net/11511/34877

Journal

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

DOI

https://doi.org/10.1016/j.jmaa.2007.03.010

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet, “On the reduction principle for differential equations with piecewise constant argument of generalized type,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, pp. 646–663, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34877.