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Sbornik: Mathematics, 2001, Volume 192, Issue 7, Pages 1035–1052
DOI: https://doi.org/10.1070/SM2001v192n07ABEH000582 (Mi sm582) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Interlaced branching equations in the theory of non-linear equations

N. A. Sidorov, V. R. Abdullin

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
English version PDF (223 kB) Citations (6)
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DOI: https://doi.org/10.1070/SM2001v192n07ABEH000582
Abstract: Necessary conditions for inheriting the interlacing property of a non-linear equation by the branching system are obtained. The case when the pair of linear operators interlacing the equation consists of projections or parametric families of linear operators is considered. New conditions are presented which allow one to reduce the number of the equations in the branching system and extend the range of applications of the method of successive approximations in the branching theory of non-linear equations. Solutions depending on free parameters belonging to certain hypersurfaces in Euclidean spaces are considered. The results obtained add to and extend earlier results on the applications of group analysis in branching theory.
Received: 31.01.2000 and 14.02.2001
Russian version:
Matematicheskii Sbornik, 2001, Volume 192, Number 7, Pages 107–124
DOI: https://doi.org/10.4213/sm582
Bibliographic databases:
UDC: 517.988.67
MSC: Primary 47J25, 47G15; Secondary 37G40
Language: English
Original paper language: Russian
Citation: N. A. Sidorov, V. R. Abdullin, “Interlaced branching equations in the theory of non-linear equations”, Mat. Sb., 192:7 (2001), 107–124; Sb. Math., 192:7 (2001), 1035–1052
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
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    References:33
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