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The Invertibility of Linear Stationary Systems of Neutral Type

The Invertibility of Linear Stationary Systems of Neutral Type Differential Equations, Vol. 38, No. 7, 2002, pp. 925–932. Translated from Differentsial'nye Uravneniya, Vol. 38, No. 7, 2002, pp. 875–881. Original Russian Text Copyright c 2002 by Boiko, Minyuk, Tsekhan. ORDINARY DIFFERENTIAL EQUATIONS The Invertibility of Linear Stationary Systems of Neutral Type V. K. Boiko, S. A. Minyuk, and O. B. Tsekhan Grodno State University, Grodno, Belarus Received November 10, 2000 INTRODUCTION A functional-di erential system is said to be invertible if the previous states of the system can be reconstructed from its current state. This de nition was rst introduced in [1, p. 64 of the Russian translation]. For ordinary di erential equations, this property follows from the unique solvability of the initial value problem. The situation is substantially di erent in the case of a delay system. For linear stationary delay systems (with one delay or several commensurable delays), the invertibility, as well as the dual property of completeness, was considered in [2, 3]. Parametric criteria for these properties were also proved there. The notion of invertibility introduced in [2] cannot be directly transferred to systems of neutral type, since the corresponding operator of internal superposition [4, p. 20] is not necessarily a completely continuous operator. Preliminary http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The Invertibility of Linear Stationary Systems of Neutral Type

Boiko, V.; Minyuk, S.; Tsekhan, O.
Differential Equations , Volume 38 (7) – Oct 10, 2004
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2002 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1021143226962
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 38, No. 7, 2002, pp. 925–932. Translated from Differentsial'nye Uravneniya, Vol. 38, No. 7, 2002, pp. 875–881. Original Russian Text Copyright c 2002 by Boiko, Minyuk, Tsekhan. ORDINARY DIFFERENTIAL EQUATIONS The Invertibility of Linear Stationary Systems of Neutral Type V. K. Boiko, S. A. Minyuk, and O. B. Tsekhan Grodno State University, Grodno, Belarus Received November 10, 2000 INTRODUCTION A functional-di erential system is said to be invertible if the previous states of the system can be reconstructed from its current state. This de nition was rst introduced in [1, p. 64 of the Russian translation]. For ordinary di erential equations, this property follows from the unique solvability of the initial value problem. The situation is substantially di erent in the case of a delay system. For linear stationary delay systems (with one delay or several commensurable delays), the invertibility, as well as the dual property of completeness, was considered in [2, 3]. Parametric criteria for these properties were also proved there. The notion of invertibility introduced in [2] cannot be directly transferred to systems of neutral type, since the corresponding operator of internal superposition [4, p. 20] is not necessarily a completely continuous operator. Preliminary

Journal

Differential Equations – Springer Journals

Published: Oct 10, 2004

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