| Contents |
| \begin{document}
\begin{abstract}
In this paper we consider the question of nonexistence of positive supersolutions
of the equation $-\De u =f(u)$ in exterior domains of $\R^N$. When $N\ge 3$, we find that positive
supersolutions exist if and only if
$$
\int_0^\de \frac{f(t)}{t^\frac{2(N-1)}{N-2}} dt 0.$ A similar condition is found for $N=2$:
$$
\int_M ^\infty e^{at} f(t) dt0$. The proofs are extended to consider some more general operators,
which include the Laplacian with gradient terms, the $p-$Laplacian or uniformly elliptic fully nonlinear
operators with radial symmetry, like the Pucci's maximal operators $\mathcal{M}_{\la,\Lambda}^\pm$,
with $\Lambda >\la>0$.
\end{abstract}
\end{document} |
|