On the uniqueness of sign changing bound state solutions of a semilinear equation
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4 , p. 599-621
doi : 10.1016/j.anihpc.2011.04.002
URL stable : http://www.numdam.org/item?id=AIHPC_2011__28_4_599_0

We establish the uniqueness of the higher radial bound state solutions of Δu+f(u)=0,x n .(P) We assume that the nonlinearity $f\in C\left(-\infty ,\infty \right)$ is an odd function satisfying some convexity and growth conditions, and has one zero at $b>0$, is nonpositive and not-identically 0 in $\left(0,b\right)$, positive in $\left[b,\infty \right)$, and is differentiable in $\left(0,\infty \right)$.

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