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

We consider the problem{−Δu+λu=up in Au>0 in Au=0 on ∂A where A is an annulus in RN, N≥2, p∈(1,+∞) and λ∈[0,+∞). Recent results ensure that there exists a sequence {pk} of exponents (pk→+∞) 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 K1 and K2 of O(N−1)-invariant functions that allow to separate the branches of bifurcating solutions getting their unboundedness.