Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 135–138 (Mi into183)  
Exact conditions of oscillation of solutions to differential equations with several delays

K. M. Chudinov

Perm State National Research Polytechnical University
Full-text PDF (260 kB)
Abstract: We obtain new nonimprovable conditions of oscillation of all solutions to a linear differential equation with several variable delays and positive coefficients. These condition have the form of the upper and lower limits of the sum of integrals of the coefficients over the sets that are determined only by the delay corresponding to this coefficient. These results differ from the well-known results in which a coarsening of the integration set is assumed.
Keywords: differential equation with several delays, oscillation, effective condition.
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 790–793
DOI: https://doi.org/10.1007/s10958-018-3791-3
Bibliographic databases:
Document Type: Article
UDC: 517.929
MSC: 34K06, 34K11
Language: Russian
Citation: K. M. Chudinov, “Exact conditions of oscillation of solutions to differential equations with several delays”, 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, 135–138; J. Math. Sci. (N. Y.), 230:5 (2018), 790–793
Citation in format AMSBIB
\Bibitem{Chu17}
\by K.~M.~Chudinov
\paper Exact conditions of oscillation of solutions to differential equations with several delays
\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 135--138
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into183}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801403}
\zmath{https://zbmath.org/?q=an:1393.34072}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 790--793
\crossref{https://doi.org/10.1007/s10958-018-3791-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044483790}
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