A global bifurcation result for a semilinear elliptic equation

We consider the problem{−Δu=up+λuin A,u>0in A,u=0on ∂A, where A   is an annulus of RNRN, N⩾2N⩾2, p∈(1,+∞)p∈(1,+∞) and λ∈(−∞,0]λ∈(−∞,0]. Recent results (Gladiali et al., 2009 [5]) ensure that there exists a sequence of values of the exponent {pk}{pk} 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.