Liouville's theorem and comparison results for solutions of degenerate elliptic equations in exterior domains

Abstract A version of Liouville's theorem is proved for solutions of some degenerate elliptic equations defined in R n \ K , where K is a compact set, provided the structure of this equation and the dimension n are related. Theoretical and numerical examples are given. Furthermore, a comparison result and the uniqueness of solution are obtained for such equations in exterior domains.