Existence and nonexistence of solutions for elliptic inequalities involving gradient terms and weights

In this paper we prove existence and nonexistence theorems for positive so- lutions of elliptic inequalities for general quasilinear operators, including m-Laplacian, mean curvature and generalized mean curvature operator, in the entire RN with a re- action involving power type gradient terms and positive weights, possibly singular or degenerate. A complete picture for the exponents involved is given. The proof technique is based on cumbersome integral a priori estimates, in the spirit of the nonlinear capacity method. No maximum principle or growth conditions at infinity for the solutions are required.