This article is cited 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

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.

UDC: 517.988.67

MSC: Primary 47J25, 47G15; Secondary 37G40

Received: 31.01.2000 and 14.02.2001

DOI: 10.4213/sm582

 English version: Sbornik: Mathematics, 2001, 192:7, 1035–1052

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