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 Sibirsk. Mat. Zh., 2013, Volume 54, Number 6, Pages 1368–1379 (Mi smj2502)

Two-sided estimates for solutions to the Cauchy problem for Wazewski linear differential systems with delay

N. V. Pertsev

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Omsk, Russia

Abstract: The Cauchy problem is considered for Wazewski linear differential systems with finite delay. The right-hand sides of systems contain nonnegative matrices and diagonal matrices with negative diagonal entries. The initial data are nonnegative functions. The matrices in equations are such that the zero solution is asymptotically stable. Two-sided estimates for solutions to the Cauchy problem are constructed with the use of the method of monotone operators and the properties of nonsingular M-matrices. The estimates from below and above are zero and exponential functions with parameters determined by solutions to some auxiliary inequalities and equations. Some estimates for solutions to several particular problems are constructed.

Keywords: Wazewski linear differential systems with delay, exponential stability, Sevast’yanov–Kotelyanskii criterion, exponential estimate, M-matrix, quasinonnegative matrix, Perron root.

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English version:
Siberian Mathematical Journal, 2013, 54:6, 1088–1097

Bibliographic databases:

UDC: 517.929

Citation: N. V. Pertsev, “Two-sided estimates for solutions to the Cauchy problem for Wazewski linear differential systems with delay”, Sibirsk. Mat. Zh., 54:6 (2013), 1368–1379; Siberian Math. J., 54:6 (2013), 1088–1097

Citation in format AMSBIB
\Bibitem{Per13} \by N.~V.~Pertsev \paper Two-sided estimates for solutions to the Cauchy problem for Wazewski linear differential systems with delay \jour Sibirsk. Mat. Zh. \yr 2013 \vol 54 \issue 6 \pages 1368--1379 \mathnet{http://mi.mathnet.ru/smj2502} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184101} \transl \jour Siberian Math. J. \yr 2013 \vol 54 \issue 6 \pages 1088--1097 \crossref{https://doi.org/10.1134/S0037446613060153} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000329110700015} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84891282549} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Dong Ya., Zhang Ya., Zhang X., “Design of Observer-Based Feedback Control For a Class of Discrete-Time Nonlinear Systems With Time-Delay”, Appl. Comput. Math., 13:1 (2014), 107–121
2. N. V. Pertsev, “Study of solutions of a continuous-discrete model of HIV infection spread”, Russ. J. Numer. Anal. Math. Model, 31:5 (2016), 281–291
3. A. Yu. Aleksandrov, “Construction of the Lyapunov–Krasovskii functionals for some classes of positive delay systems”, Siberian Math. J., 59:5 (2018), 753–762
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