We obtain Caccioppoli — type estimates for nontrivial and nonnegative solutions to the anticoercive partial differential inequalities of elliptic type involving degenerated p — Laplacian: $-Δ_{p,a} u:= -\mathrm{div}(a(x)|\na u|^{p-2}\na u)\ge b(x)Φ(u)$, where u is defined in a ...