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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 5, Pages 53–61 (Mi ivm7303)  
This article is cited in 12 scientific papers (total in 12 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
Full-text PDF (208 kB) Citations (12)
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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.
Received: 22.12.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 5, Pages 43–50
DOI: https://doi.org/10.3103/S1066369X11050070
Bibliographic databases:
Document Type: Article
UDC: 517.91+517.98
Language: Russian
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
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\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
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\mathscinet{http://mathscinet.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}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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