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On the Conditions for Oscillation of the Solutions to Differential Equations with Aftereffect and Generalization of the Koplatadze-Chanturiya Theorem

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Abstract

We consider a nonautonomous first-order linear differential equation with several delays and nonnegative coefficients. Some new sufficient conditions for the oscillation of all solutions are obtained in the form of an estimate for the lower limit of the sum of integrals of the coefficients. For the equation with one delay, the obtained oscillation conditions sharpen the classical Koplatadze-Chanturiya Theorem. The difference in strength between the new and available oscillation conditions is more significant for the equation with several delays.

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Authors and Affiliations

  1. Research Center Functional-Differential Equations, Perm National Research Polytechnic University, Perm, Perm Krai, Russia

    K. M. Chudinov

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  1. K. M. Chudinov
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Correspondence to K. M. Chudinov.

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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 224–233.

The author was supported by the Ministry for Education and Science of the Russian Federation by the State Assignment No. 1.5336.2017/8.9 with the support of the Russian Foundation for Basic Research (Grant 18-01-00928).

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Chudinov, K.M. On the Conditions for Oscillation of the Solutions to Differential Equations with Aftereffect and Generalization of the Koplatadze-Chanturiya Theorem. Sib Math J 61, 178–186 (2020). https://doi.org/10.1134/S0037446620010152

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  • DOI: https://doi.org/10.1134/S0037446620010152

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