Abstract
We consider the Cauchy problem for a class of nonlinear systems of differential equations of large dimension, establish some properties of solutions, and prove that for a sufficiently large number of differential equations the last component of the solution is an approximate solution to the initial value problem for a delay differential equation.
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Original Russian Text Copyright © 2012 Matveeva I. I. and Mel’nik I. A.
The authors were supported by the Russian Foundation for Basic Research (Grant 10-01-00035), the Federal Target Program “Scientific and Educational Personnel of Innovative Russia” for 2009–2013 (State Contract 16.740.11.0127), and the Interdisciplinary Project of the Siberian Branch of the Russian Academy of Sciences (Grant 107).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 2, pp. 312–324, March–April, 2012.
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Matveeva, I.I., Mel’nik, I.A. On the properties of solutions to a class of nonlinear systems of differential equations of large dimension. Sib Math J 53, 248–258 (2012). https://doi.org/10.1134/S0037446612020085
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DOI: https://doi.org/10.1134/S0037446612020085