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We consider the elliptic system
$$
\left\{
\begin{array}{l}
-\Delta u + |\nabla u |^q = \lambda v^p\\
-\Delta v + |\nabla v |^q = \mu u^s
\end{array}
\right.
\qquad \hbox{in } \mathbb{R}^N \setminus B_{R_0},
$$
where $N\ge 3$, $q>1$, $p,s>0$, $\lambda,\mu>0$. We are interested in analyzing the
question of nonexistence of positive supersolutions of this system. For several ranges of
the exponents involved we show that no positive supersolutions can exist. These
ranges of nonexistence turn out to be optimal in some cases. |
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