This article is cited in 3 scientific papers (total in 3 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
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.
Wazewski linear differential systems with delay, exponential stability, SevastТyanov–Kotelyanskii criterion, exponential estimate, M-matrix, quasinonnegative matrix, Perron root.
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Siberian Mathematical Journal, 2013, 54:6, 1088–1097
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
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\paper Two-sided estimates for solutions to the Cauchy problem for Wazewski linear differential systems with delay
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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