Equivariant bifurcation index
2010; Elsevier BV; Volume: 73; Issue: 9 Linguagem: Inglês
10.1016/j.na.2010.06.001
ISSN1873-5215
AutoresGabriel López Garza, Sławomir Rybicki,
Tópico(s)Geometry and complex manifolds
ResumoWe 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: BIFG(νk0−1)≠Θ∈U(G) iff BIFT(νk0−1)≠Θ∈U(T), 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 {−Δu=f(u,λ)inBn,u=0onSn−1, are global bifurcation points. Additionally, the global symmetry breaking bifurcation points are characterised.
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