A remark on entire solutions of quasilinear elliptic equations

By applying a main comparison theorem of Pucci and Serrin (2007) 2] we cover, for general equations of p-Laplace type, the open cases of Theorems B, D, E of Farina and Serrin (submitted for publication) 1] as described in Problems 2 and 3 of Section 12 of Farina and Serrin (submitted for publication) 1]. Moreover, we provide significant improvements of Theorem C and Theorem 5 of Farina and Serrin (submitted for publication) 1], the latter in the context of mean curvature type operators, see Theorem 1.3 and Theorems 5.2-5.4 below.Finally, Theorem 1.1 provides a new Liouville theorem outside the context of work in Farina and Serrin (submitted for publication) 1].