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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