| Abstract: |
| We consider radial singular solutions of the semilinear elliptic equation
$\Delta u + f(u) = 0$ in $\Omega\setminus\{0\}$, where
$\Omega$ is a unit ball in ${\bf R}^N$ with $N \geq 3$ and $f \in C^2[0, \infty)$.
We will show some qualitative properties of the singular solutions
with general supercritical nonlinearities.
Our method can treat a wide class of nonlinearities $f(u)$ in a unified way,
e.g., $u^p\log u$, $\exp(u^p)$ and $\exp(\cdots\exp(u)\cdots)$ as well as $u^p$ and $e^u$.
We will verify an exact asymptotic expansion of the singular solution
as well as its uniqueness in the space of radial functions. |
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