On the uniqueness of sign changing bound state solutions of a semilinear equation

Cortázar, Carmen; García-Huidobro, Marta; Yarur, Cecilia S.

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4, pp. 599-621.

We establish the uniqueness of the higher radial bound state solutions of

$$\begin{array}{cc}\Delta u+f\left(u\right)=0,x\in {ℝ}^n.& \text{(P)}\end{array}$$

We assume that the nonlinearity $f\in C(-\infty ,\infty )$ is an odd function satisfying some convexity and growth conditions, and has one zero at $b>0$, is nonpositive and not-identically 0 in $(0,b)$, positive in $[b,\infty )$, and is differentiable in $(0,\infty )$.

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