Abstract

We establish the uniqueness of the second radial bound state solution of(P)? u + f (u) = 0, x ? Rn . We assume that the nonlinearity f ? C (- 8, 8) is an odd function satisfying some convexity and growth conditions of superlinear type, and either has one zero at b > 0, is nonpositive and not identically 0 in (0, b), and is differentiable and positive [b, 8), or is positive and differentiable in [0, 8). © 2009 Elsevier Masson SAS. All rights reserved.