| Abstract: |
| 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
$$
\mbox{div}\big(\mathsf A\,\nabla v\big)+\mathsf B\,f(v)=0\,,\quad\lim_{|x|\to+\infty}v(x)=0,\quad x\in\mathbb R^n,\eqno{(P)}
$$
$n>2$, where $\mathsf A$ and $\mathsf B$ are two positive, radial, smooth functions defined on $\mathbb R^n\setminus\{0\}$.
We assume that the nonlinearity $f\in C(-c,c)$, $00$,
is non positive and not identically 0 in $(0,b)$, positive in $(b,c)$, and is differentiable in $(0,c)$. |
|