Global bifurcations of critical orbits of G -invariant strongly indefinite functionals

Let H be a separable Hilbert space which is an orthogonal representation of a compact Lie group G and let Φ : H → R be a G -invariant strongly indefinite functional of the class C 1 . To study critical orbits of Φ we have defined the degree for G -invariant strongly indefinite functionals, which is an element of the Euler ring U ( G ) . Using this degree we have formulated the Rabinowitz alternative for G -invariant strongly indefinite functionals. The abstract results are applied to the study of global bifurcations of weak solutions of non-cooperative systems of elliptic differential equations.