| Abstract: |
| We consider radial solutions of a general elliptic equation involving a weighted Laplace operator with a subcritical nonlinearity.
We establish the uniqueness of the higher radial bound state solutions
$$
\mbox{div}\big(\mathsf a\,\nabla u\big)+\mathsf b\,f(u)=0\,,\quad\lim_{|x|\to+\infty}u(x)=0,\eqno{(P)}
$$
where $\mathsf a$ and $\mathsf b$ are two positive, radial, smooth functions defined on $\R^d\setminus\{0\}$ and $f\in C(\R)$ satisfying some growth conditions.
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 $u_0>0$,
is non positive and not identically 0 in $(0,u_0)$, positive in $[u_0,\infty)$, and is differentiable in $(0,\infty)$. |
|