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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 68–73 (Mi into168)  
Oscillation criterion for autonomous differential equations with bounded aftereffect

V. V. Malygina

Perm State National Research Polytechnical University
Full-text PDF (271 kB)
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.
Keywords: differential equation with aftereffect, oscillation, concentrated and distributed delay.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1890, áàçîâàÿ ÷àñòü çàäàíèÿ 2014/152
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 717–723
DOI: https://doi.org/10.1007/s10958-018-3776-2
Bibliographic databases:
Document Type: Article
UDC: 517.929
MSC: 34K06, 34K11
Language: Russian
Citation: V. V. Malygina, “Oscillation criterion for autonomous differential equations with bounded aftereffect”, Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 132, VINITI, Moscow, 2017, 68–73; J. Math. Sci. (N. Y.), 230:5 (2018), 717–723
Citation in format AMSBIB
\Bibitem{Mal17}
\by V.~V.~Malygina
\paper Oscillation criterion for autonomous differential equations with bounded aftereffect
\inbook Proceedings of International Symposium “Differential Equations–2016”, Perm, May 17-18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 132
\pages 68--73
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into168}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801388}
\zmath{https://zbmath.org/?q=an:1392.34083}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 717--723
\crossref{https://doi.org/10.1007/s10958-018-3776-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044450132}
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