Abstract
For autonomous functional-differential equations with delays, we obtain an oscillation criterion, which allows one to reduce the oscillation problem to the calculation of a unique root of a real-valued function determined by the coefficients of the original equation. The criterion is illustrated by examples of equations with concentrated and distributed aftereffect, for which convenient oscillation tests are obtained.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.
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Malygina, V.V. Oscillation Criterion for Autonomous Differential Equations with Bounded Aftereffect. J Math Sci 230, 717–723 (2018). https://doi.org/10.1007/s10958-018-3776-2
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DOI: https://doi.org/10.1007/s10958-018-3776-2