Radial solutions to a dirichlet problem involving critical exponents when N = 6

In this paper we show that, for each λ > 0, the set of radially symmetric solutions to the boundary value problem -Δu(x) = λu(x) + u(x)|u(x)|, x ∈ B:= {x ∈ R6 : ||x|| < 1}, u(x) = 0, x ∈ ∂B, is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity. © 1996 American Mathematical Society.