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

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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 6, Pages 1368–1379 (Mi smj2502)

This article is cited in 12 scientific papers (total in 12 papers)

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

Full-text PDF (322 kB) Citations (12)

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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.

Received: 17.12.2012

English version:
Siberian Mathematical Journal, 2013, Volume 54, Issue 6, Pages 1088–1097
DOI: https://doi.org/10.1134/S0037446613060153

Bibliographic databases:

Document Type: Article

UDC: 517.929

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/smj2502

https://www.mathnet.ru/eng/smj/v54/i6/p1368

This publication is cited in the following 12 articles:

N. V. Pertsev, “Ustoichivost reshenii lineinykh sistem differentsialnykh uravnenii dinamiki populyatsii s peremennym zapazdyvaniem”, Matem. tr., 27:3 (2024), 74–98
N. V. Pertsev, “Primenenie differentsialnykh uravnenii s peremennym zapazdyvaniem v kompartmentnykh modelyakh zhivykh sistem”, Sib. zhurn. industr. matem., 24:3 (2021), 55–73
N. V. Pertsev, K. K. Loginov, “Nakhozhdenie parametrov eksponentsialnykh otsenok reshenii zadachi Koshi dlya nekotorykh sistem lineinykh differentsialnykh uravnenii s zapazdyvaniem”, Sib. elektron. matem. izv., 18:2 (2021), 1307–1318
N. V. Pertsev, “Application of Differential Equations with Variable Delay in the Compartmental Models of Living Systems”, J. Appl. Ind. Math., 15:3 (2021), 466
K. K. Loginov, N. V. Pertsev, “Asymptotic Behavior of Solutions to a Delay Integro-Differential Equation Arising in Models of Living Systems”, Sib. Adv. Math., 31:2 (2021), 131
N. V. Pertsev, K. K. Loginov, V. A. Topchii, “Analysis of an epidemic mathematical model based on delay differential equations”, J. Appl. Industr. Math., 14:2 (2020), 396–406
N. V. Pertsev, “Exponential decay estimates for some components of solutions to the nonlinear delay differential equations of the living system models”, Siberian Math. J., 61:4 (2020), 715–724
K. K. Loginov, N. V. Pertsev, “Asimptoticheskoe povedenie reshenii integro-differentsialnogo uravneniya s zapazdyvaniem, voznikayuschego v modelyakh zhivykh sistem”, Matem. tr., 23:2 (2020), 122–147
N. V. Pertsev, “Matrichnye kriterii ustoichivosti i neustoichivosti nekotorykh sistem lineinykh differentsialnykh uravnenii s zapazdyvaniem”, Sib. elektron. matem. izv., 16 (2019), 876–885
A. Yu. Aleksandrov, “Construction of the Lyapunov–Krasovskii functionals for some classes of positive delay systems”, Siberian Math. J., 59:5 (2018), 753–762
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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