On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms

In this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form div { g ( | x | ) | D u | p − 2 D u } ⩾ h ( | x | ) f ( u ) ± h ˜ ( | x | ) ℓ ( | D u | ) , under the main request that h and h ˜ are continuous on R + . We achieve our conclusions introducing a generalized version of the well-known Keller–Osserman condition.