| Contents |
| We consider the problem
$$u''(r)+ \frac{f'(r)}{f(r)}u'(r)-g(r)u(r)+h(r)|u(r)|^{p-1}u(r)=0,
\quad r\in (0,R)$$
and $u(0)\in {\mathbb R}$, $u(R)=0$,
where $R\in (0,\infty]$, $p>1$ and
$f,g,h$ are appropriate functions.
In the case of $R=\infty$, $u(R)=\infty$ means
$u(r)\rightarrow 0$ as $r\rightarrow\infty$.
We study the uniqueness of positive solutions of the problem
and we apply it to various examples.
We also study its nondegeneracy not only in radial spaces
but also in nonradial spaces.
This is a joint work with Kohtaro Watanabe. |
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