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Sib. Zh. Ind. Mat., 2012, Volume 15, Number 1, Pages 132–137 (Mi sjim717)  

This article is cited in 2 scientific papers (total in 2 papers)

Successive approximations to solutions of nonlinear equations with vector parameter in the irregular case

N. A. Sidorovab, D. N. Sidorovba, R. Yu. Leont'evba

a Institute of Energy Systems SB RAS, Irkutsk, RUSSIA
b Irkutsk State University, Irkutsk, RUSSIA

Abstract: We consider a nonlinear operator equation with a Fredholm operator in the principal part. The nonlinear part of the equation depends on some functionals that are defined on an open set of a normed linear space. We suggest a method of successive asymptotic approximations to branching solutions. We apply this method to study a nonlinear boundary value problem describing the oscillation of a satellite in the plane of its elliptic orbit.

Keywords: branching of solutions, Fredholm operator, asymptotics, Trenogin's regularizer, successive approximations.

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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:3, 387–392

Bibliographic databases:

UDC: 517.988.7
Received: 05.05.2011

Citation: N. A. Sidorov, D. N. Sidorov, R. Yu. Leont'ev, “Successive approximations to solutions of nonlinear equations with vector parameter in the irregular case”, Sib. Zh. Ind. Mat., 15:1 (2012), 132–137; J. Appl. Industr. Math., 6:3 (2012), 387–392

Citation in format AMSBIB
\Bibitem{SidSidLeo12}
\by N.~A.~Sidorov, D.~N.~Sidorov, R.~Yu.~Leont'ev
\paper Successive approximations to solutions of nonlinear equations with vector parameter in the irregular case
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 1
\pages 132--137
\mathnet{http://mi.mathnet.ru/sjim717}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3112340}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 3
\pages 387--392
\crossref{https://doi.org/10.1134/S1990478912030143}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Sidorov, “Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov–Maxwell system”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 6:4 (2013), 85–106  mathnet
    2. Falaleev V M., Romanova O.A., Sinitsyn V A., Dreglea I A., Leont'ev R.Yu., Sidorov D.N., “on the Occasion of the 80Th Birthday of Professor N. a. Sidorov”, Bull. Irkutsk State Univ.-Ser. Math., 32 (2020), 134–143  crossref  mathscinet  zmath  isi
  • Сибирский журнал индустриальной математики
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