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Global Solvability and Estimates of Solutions to the Cauchy Problem for the Retarded Functional Differential Equations That Are Used to Model Living Systems

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Abstract

We study the Cauchy problem for the retarded functional differential equations that model the dynamics of some living systems. We find certain conditions ensuring the existence, uniqueness, and nonnegativity of solutions on finite and infinite time intervals. We obtain upper bounds for solutions and prove the continuous dependence of solutions on the initial data on finite time intervals.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Omsk Branch, Omsk, Russia

    N. V. Pertsev

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  1. N. V. Pertsev
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Correspondence to N. V. Pertsev.

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Original Russian Text Copyright © 2018 Pertsev N.V.

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 59, No. 1, pp. 143–157, January–February, 2018; DOI: 10.17377/smzh.2018.59.113

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Pertsev, N.V. Global Solvability and Estimates of Solutions to the Cauchy Problem for the Retarded Functional Differential Equations That Are Used to Model Living Systems. Sib Math J 59, 113–125 (2018). https://doi.org/10.1134/S0037446618010135

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  • DOI: https://doi.org/10.1134/S0037446618010135

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