Radially symmetric solutions to a dirichlet problem involving critical expone

In this paper we answer, for N = 3, 4, the question raised in [1] on the number of radially symmetric solutions to the boundary value problem where Δ is the Laplacean operator and λ >0. Indeed, we prove that if N = 3, 4, then for any λ >0 this problem has only finitely many radial solutions. For N = 3, 4, 5 we show that, for each λ >0, the set of radially symmetric solutions is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity. © 1994 American Mathematical Society.