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 A is the Laplacean operator and X > 0 . Indeed, we prove that if N = 3, 4 , then for any A > 0 this problem has only finitely many radial solutions. For N = 3, 4, 5 we show that, for each X > 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.