Abstract
We establish some new effective oscillation conditions for solutions to linear delay differential equations of the first order. We develop a new approach to obtaining oscillation conditions in the form of the upper limit of a function of equation parameters. We apply the proposed approach to equations with one and several concentrated delays and to those with a distributed delay. We demonstrate the advantages of the obtained results over the well-known ones.
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 7, pp. 72–85.
Funding
This work was performed within the framework of the main part of the state task of the Ministry of Education and Science of the Russian Federation (project no. 1.5336.2017/8.9) and supported by the Russian Foundation for Basic Research (project no. 18-01-00928).
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Chudinov, K.M., Malygina, V.V. Oscillation Criteria for Solutions of Delay Differential Equations of the First Order. Russ Math. 63, 62–74 (2019). https://doi.org/10.3103/S1066369X19070077
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DOI: https://doi.org/10.3103/S1066369X19070077