Accession Number : ADA141709

Title :   Morse Theory for Symmetric Functionals on the Sphere and an Application to a Bifurcation Problem.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Benci,V ; Pacella,F

PDF Url : ADA141709

Report Date : Apr 1984

Pagination or Media Count : 22

Abstract : This paper uses Conley's index to study the cortical points of a function f on a finite dimensional sphere in presence of a symmetry group. The authors prove a theorem which leads to a lower bound on the number of critical points of f when the group is finite, even if the action is not free. This investigation has been motivated by the following bifurcation problem Au = lambda, where A is a variational G-equivariant operator. An estimated on the number of 'branches' bifurcating from an eigenvalue of A'(0) is given. (Author)

Descriptors :   *Bifurcation(Mathematics), *Points(Mathematics), Variational methods, Hilbert space, Symmetry, Operators(Mathematics), Estimates, Eigenvalues, Spheres

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE