
This article is cited in 3 scientific papers (total in 3 papers)
Twosided 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 righthand 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. Twosided estimates for solutions to the Cauchy problem are constructed with the use of the method of monotone operators and the properties of nonsingular Mmatrices. 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, Mmatrix, quasinonnegative matrix, Perron root.
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English version:
Siberian Mathematical Journal, 2013, 54:6, 1088–1097
Bibliographic databases:
UDC:
517.929 Received: 17.12.2012
Citation:
N. V. Pertsev, “Twosided 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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