  This work is devoted to the study of a Liouville comparison principle for
entire weak solutions of quasilinear differential inequalities of the form
$A(u) + |u|^{q-1}u \leq A(v) + |v|^{q-1}v$ on ${\Bbb R}^n$, where $n\geq 1$,
$q$ is positive, and the operator $A(w)$ belongs to a class of the so-called
$\alpha$-monotone operators. Typical examples of such operators are the
$p$-Laplacian and its well-known modifications. The results improve and
supplement those in [1].
