Equations Whose Sets of Solutions are Invariant Under a Group of Mappings Isomorphic to a One-Parameter Group of Rotations

We construct classes of systems of equations whose sets of solutions are invariant under a group of mappings isomorphic to a one-parameter group of rotations. It is shown that unbounded solutions of these systems are unstable. We also present the applications of obtained results to the problems of n...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-08, Vol.256 (5), p.689-702
Main Author: Slyusarchuk, V. Yu
Format: Article
Language:English
Subjects:
Invariants
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:We construct classes of systems of equations whose sets of solutions are invariant under a group of mappings isomorphic to a one-parameter group of rotations. It is shown that unbounded solutions of these systems are unstable. We also present the applications of obtained results to the problems of nonlinear mechanics.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05453-9