Unbounded sets of solutions of non-cooperative elliptic systems on spheres

The aim of this paper is to show that any continuum of nontrivial solutions of a non-cooperative system of elliptic equations on the sphere Sn−1Sn−1, bifurcating from the set of trivial solutions, is unbounded. Moreover, we characterize bifurcation points of this system at which the global symmetry-breaking phenomenon occurs. As the main tool we use the degree for SO(2)SO(2)-invariant strongly indefinite functionals defined in [13].