On properties of solutions of quasilinear second-order elliptic inequalities

Let Omega be an unbounded open subset of Rn, n >= 2, and A : Omega x R-n -> R-n be a function such that C-1 vertical bar zeta vertical bar(p) <= zeta A(x,zeta), vertical bar A(x,zeta)vertical bar <= C-2 vertical bar zeta vertical bar(p-1) with some constants C-1 > 0, C-2 > 0, and p >1 for almost all x is an element of Omega and for all zeta is an element of R-n we obtain blow-up conditions and priori estimates fro inequalities of the form div A(x, Du) + b(x)vertical bar Du vertical bar(alpha) >= q(x)g(u) in Omega, where p - 1 <= alpha <= p is a real number and b, q, and g are non-negative functions. (C) 2015 Elsevier Ltd. All rights reserved.