Separation of branches of O(N-1)-invariant solutions for a semilinear elliptic equation

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.