We consider the quasilinear elliptic equation                                -Δu + H(x, u, Du) = ƒ, in Ω    (EH)being Ω ⊂ℝN, N ≥1, an open set with regular bounded boundary and f ∈ L∞(Ω). In this work we obtain upper estimates of the growth, near to the boundary, for any classic solution of (EH) and the exact behavior for any non negative solution of (EH) verifiying                            Finally, we prove the uniqueness of blow-up solutions of (EH).