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 61–63 (Mi into166)  
On a certain first-order differential equation with delay

A. S. Larionov

Bratsk State University
Full-text PDF (256 kB)
Abstract: We consider the Cauchy problem for a first-order quasilinear differential equation with delayed argument of neutral type, and obtain sufficient conditions of the existence and uniqueness of its solutions. Proofs of the solvability of nonlinear problems, estimates of solutions, and constructions of approximate methods are based on Chaplygin-type theorems on differential inequalities.
Keywords: differential equation, delay , monotonic operator, problem Cauchy, solvability.
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 708–711
DOI: https://doi.org/10.1007/s10958-018-3774-4
Bibliographic databases:
Document Type: Article
UDC: 517.927.4, 517.929.7
MSC: 34K10, 34K40
Language: Russian
Citation: A. S. Larionov, “On a certain first-order differential equation with delay”, 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, 61–63; J. Math. Sci. (N. Y.), 230:5 (2018), 708–711
Citation in format AMSBIB
\Bibitem{Lar17}
\by A.~S.~Larionov
\paper On a certain first-order differential equation with delay
\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 61--63
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into166}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801386}
\zmath{https://zbmath.org/?q=an:1393.34078}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 708--711
\crossref{https://doi.org/10.1007/s10958-018-3774-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044451397}
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