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Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 5, Pages 53–61 (Mi ivm7303)  

This article is cited in 11 scientific papers (total in 11 papers)

Small solutions of nonlinear differential equations near branching points

N. A. Sidorovab, D. N. Sidorovc

a Chair of Mathematical Analysis and Differential Equations, Irkutsk State University, Irkutsk, Russia
b Institute of Systems Dynamics and Control Theory, Irkutsk, Russia
c Department of Applied Mathematics, Institute of Energy Systems, Siberian Branch of Russian Acedemy of Sciences, Irkutsk, Russia

Abstract: We construct parametric families of small branching solutions to nonlinear differential equations of the $n$th order near branching points. We use methods of the analytical theory of branching solutions of nonlinear equations and the theory of differential equations with a regular singular point. We illustrate the general existence theorems with an example of a nonlinear differential equation in a certain magnetic insulation problem.

Keywords: Newton diagram, Jordan forms, Euler operator, branching, contracted mapping.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:5, 43–50

Bibliographic databases:

UDC: 517.91+517.98
Received: 22.12.2009

Citation: N. A. Sidorov, D. N. Sidorov, “Small solutions of nonlinear differential equations near branching points”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 5, 53–61; Russian Math. (Iz. VUZ), 55:5 (2011), 43–50

Citation in format AMSBIB
\Bibitem{SidSid11}
\by N.~A.~Sidorov, D.~N.~Sidorov
\paper Small solutions of nonlinear differential equations near branching points
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 5
\pages 53--61
\mathnet{http://mi.mathnet.ru/ivm7303}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2920089}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 5
\pages 43--50
\crossref{https://doi.org/10.3103/S1066369X11050070}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051612096}


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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, D. N. Sidorov, “O posledovatelnykh priblizheniyakh reshenii vyrozhdennoi zadachi Koshi”, Tr. IMM UrO RAN, 18, no. 2, 2012, 238–244  mathnet  elib
    2. D. N. Sidorov, “O semeistvakh reshenii integralnykh uravnenii Volterry pervogo roda s razryvnymi yadrami”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 12, 44–52  mathnet
    3. D. N. Sidorov, “O razreshimosti uravnenii Volterra I roda s kusochno-nepreryvnymi yadrami v klasse obobschennykh funktsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:1 (2012), 80–95  mathnet
    4. D. N. Sidorov, “Solvability of systems of integral Volterra equations of the first kind with piecewise continuous kernels”, Russian Math. (Iz. VUZ), 57:1 (2013), 54–63  mathnet  crossref
    5. Sidorov D.N., “On Parametric Families of Solutions of Volterra Integral Equations of the First Kind with Piecewise Smooth Kernel”, Differ. Equ., 49:2 (2013), 210–216  crossref  mathscinet  mathscinet  zmath  isi  elib  elib
    6. 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
    7. N. A. Sidorov, D. N. Sidorov, “On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels”, Math. Notes, 96:5 (2014), 811–826  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. Sidorov D.N., “Generalized Solution To the Volterra Equations With Piecewise Continuous Kernels”, Bull. Malays. Math. Sci. Soc., 37:3 (2014), 757–768  mathscinet  zmath  isi
    9. N. A. Sidorov, “Classic solutions of boundary value problems for partial differential equations with operator of finite index in the main part of equation”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 55–70  mathnet  crossref
    10. Kazakov A.L., Kuznetsov P.A., “Exact Solutions of the Nonlinear Heat Conduction Model”, Bull. South Ural State U. Ser.-Math Model Program Comput., 13:4 (2020), 33–47  crossref  zmath  isi  scopus
    11. Kazakov A., Kuznetsov P., Lempert A., “Analytical Solutions to the Singular Problem For a System of Nonlinear Parabolic Equations of the Reaction-Diffusion Type”, Symmetry-Basel, 12:6 (2020), 999  crossref  isi  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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