A global bifurcation result for a semilinear elliptic equation

We consider the problem { − Δ u = u p + λ u in A , u > 0 in A , u = 0 on ∂ A , where A is an annulus of R N , N ⩾ 2 , p ∈ ( 1 , + ∞ ) and λ ∈ ( − ∞ , 0 ] . Recent results (Gladiali et al., 2009 [5]) ensure that there exists a sequence of values of the exponent { p k } at which nonradial bifurcation from the radial solution occurs. We prove the existence of global branches of nonradial solutions bifurcating from the curve of radial ones.