Classification of balanced sets and critical points of even functions on spheres
Charles V. Coffman · Transactions of the American Mathematical Society · 1991
The Lyusternik-Schnirelman approach to the study of critical points of even functionals on the sphere S N {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 {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.