In memoriam

Abstract

We consider a bifurcation index BIFG(νk0−1)∈U(G) defined in terms of the degree for G-equivariant gradient maps, see Gȩba (1997) [21], Rybicki (1994) [22], Rybicki (2005) [23], where G is a real, compact, connected Lie group and U(G) is the Euler ring of G, see tom Dieck (1977) [29], tom Dieck (1987) [30].The main result of this article is the following: where T⊂G is a maximal torus of G.It is also shown that all the bifurcation points of weak solutions of the following problem are global bifurcation points. Additionally, the global symmetry breaking bifurcation points are characterised.