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In this paper we answer, for N = 3, 4, the question raised in  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 anddoi:10.2307/2154749 fatcat:6gsei25t6rhgbfjtuggfax5qji