  We consider a semilinear elliptic problem in an annulus of R^N, with N>1.
Recent results ensure that there exists a sequence p_k of exponents of the
nonlinear term at which a nonradial bifurcation from the radial solution
occurs. Exploiting the properties of O(N-1)-invariant spherical harmonics, we
introduce two suitable cones K^1 and $K^2$ of O(N-1)-invariant functions that
allow to separate the branches of bifurcating solutions from the others,
getting the unboundedness of these branches.
