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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 132, Pages 144–148 (Mi into185)  
This article is cited in 6 scientific papers (total in 6 papers)

Autonomous Noether boundary-value problems not solved with respect to the derivative

S. M. Chujko, O. V.  Nesmelova (Starkova)

Donbass State Pedagogical University
Full-text PDF (276 kB) Citations (6)
Abstract: In monographs of N. V. Azbelev, A. M. Samoilenko, and A. A. Boichuk, constructive methods of the study of Noether boundary-value problems have been developed. These methods continue the investigation of periodic problems stated by H. Poincaré, A. M. Lyapunov, N. M. Krylov, N. N. Bogolyubov, I. G. Malkin, and O. Veivoda by methods of small parameter. We propose an improved scheme of the study of autonomous Noether boundary-value problems for nonlinear systems in critical cases. In the case of multiple roots of the equation for generating constants, we obtain sufficient conditions of the existence of solutions to an autonomous boundary-value problem not solved with respect to the derivative. The effectiveness of the scheme proposed is illustrated by an example of the periodic problem for the Liénard equation.
Keywords: autonomous boundary-value problem, ordinary differential equation, Liénard equation.
Funding agency Grant number
State Fund for Fundamental Researches (Ukraine) 0115U003182
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 230, Issue 5, Pages 799–803
DOI: https://doi.org/10.1007/s10958-018-3793-1
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 34B15
Language: Russian
Citation: S. M. Chujko, O. V. Nesmelova (Starkova), “Autonomous Noether boundary-value problems not solved with respect to the derivative”, 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, 144–148; J. Math. Sci. (N. Y.), 230:5 (2018), 799–803
Citation in format AMSBIB
\Bibitem{ChuSta17}
\by S.~M.~Chujko, O.~V.~ Nesmelova (Starkova)
\paper Autonomous Noether boundary-value problems not solved with respect to the derivative
\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 144--148
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into185}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801405}
\zmath{https://zbmath.org/?q=an:1393.34037}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 230
\issue 5
\pages 799--803
\crossref{https://doi.org/10.1007/s10958-018-3793-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85044364703}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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