  A version of Liouville's theorem is proved for solutions of some degenerate
elliptic equations defined in $\mathbb{R}^n\backslash K$, where $K$ is a
compact set, provided the structure of this equation and the dimension $n$ are
related. This result is a correction of a previous one established by Serrin,
since some additional hypotheses are necessary. Theoretical and numerical
examples are given. Furthermore, a comparison result and the uniqueness of
solution are obtained for such equations in exterior domains.
