## B. V. Loginov and O. V. Makeev

# Solutions with subgroup symmetry for singular equations in bifurcation theory

## (*Lobachevskii Journal of Mathematics, Vol.20, pp.91-101*)

In the article, on the base of abstract theory
(B. V. Loginov, 1979)
the nonlinear eigenvalue problems for nonlinearly
perturbed Helmholtz equations having application to low
temperature plasma theory and to some problems of differential
geometry are considered. Other possible often technically more
difficult applications (for instance, periodical solutions in heat
convection theory) are completely determined by the group symmetry of
original equations and do not depend on their concrete essence. In the
general case of finite group symmetry with known composition law,
a computer program for determination of all subgroups is given,
in particular, for dihedral and also planar and spatial
crystallographic groups.

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