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Mathematics of the USSR-Sbornik, 1971, Volume 14, Issue 3, Pages 438–452
DOI: https://doi.org/10.1070/SM1971v014n03ABEH002627 (Mi sm3265) 		 
This article is cited in 17 scientific papers (total in 18 papers)

The use of group properties to determine milti-parameter families of solutions of nonlinear equations

B. V. Loginov, V. A. Trenogin
English version PDF (937 kB) Citations (18)
References:
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DOI: https://doi.org/10.1070/SM1971v014n03ABEH002627
Abstract: We consider a nonlinear equation in a Banach space which is invariant relative to a continuous group. We give conditions which allow us to reduce Lyapunov–Schmidt branch equations in both the number of equations and the number of unknowns, which makes it possible to simplify significantly the search for multi-parameter families of solutions of the given problem.
Bibliography: 15 titles.
Received: 15.06.1970
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1971, Volume 85(127), Number 3(7), Pages 440–454
Bibliographic databases:
UDC: 517.93+513.881
MSC: Primary 34G05; Secondary 34B15
Language: English
Original paper language: Russian
Citation: B. V. Loginov, V. A. Trenogin, “The use of group properties to determine milti-parameter families of solutions of nonlinear equations”, Mat. Sb. (N.S.), 85(127):3(7) (1971), 440–454; Math. USSR-Sb., 14:3 (1971), 438–452
Citation in format AMSBIB
\Bibitem{LogTre71}
\by B.~V.~Loginov, V.~A.~Trenogin
\paper The use of group properties to determine milti-parameter families of solutions of nonlinear equations
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 3(7)
\pages 440--454
\mathnet{http://mi.mathnet.ru/sm3265}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=283642}
\zmath{https://zbmath.org/?q=an:0221.47040}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 3
\pages 438--452
\crossref{https://doi.org/10.1070/SM1971v014n03ABEH002627}
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  • https://www.mathnet.ru/eng/sm/v127/i3/p440
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:382
    Russian version PDF:150
    English version PDF:18
    References:42
     
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