  We consider radial solutions of a general elliptic equation involving a
weighted Laplace operator. We establish the uniqueness of the radial bound
state solutions to $$ {div}\big(\mathsf A\,\nabla v\big)+\mathsf
B\,f(v)=0\,,\quad\lim_{|x|\to+\infty}v(x)=0,\quad x\in\mathbb R^n,$$ $n>2$,
where $\mathsf A$ and $\mathsf B$ are two positive, radial, smooth functions
defined on $\mathbb R^n\setminus\{0\}$.
  We assume that the nonlinearity $f\in C(-c,c)$, $0<c\le\infty$ is an odd
function satisfying some convexity and growth conditions, and has a zero at
$b>0$, is non positive and not identically 0 in $(0,b)$, positive in $(b,c)$,
and is differentiable in $(0,c)$.
