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Classification of balanced sets and critical points of even functions on spheres


Author: Charles V. Coffman
Journal: Trans. Amer. Math. Soc. 326 (1991), 727-747
MSC: Primary 58E05; Secondary 47H99, 55M99
DOI: https://doi.org/10.1090/S0002-9947-1991-1007802-0
MathSciNet review: 1007802
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Abstract: The Lyusternik-Schnirelman approach to the study of critical points of even functionals on the sphere $ {S^N}$ employs min-max or max-min principles whose formulation uses a numerical invariant that is defined for compact balanced subsets of $ {S^N}$. The Krasnosel'skii genus is an example. Here we study a general class of such invariants (which is quite large) with particular attention to the following questions: formulation of dual variational principles, multiplicity results for critical points, and determination of the Morse index of nondegenerate critical points.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1007802-0
Article copyright: © Copyright 1991 American Mathematical Society

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