A priori estimate for a quasilinear problem depending on the gradient

The main purpose of this paper is to establish a priori estimate for positive solutions of some superlinear, quasilinear elliptic equations where the nonlinearity depends on x, u, and ∇u. Our argument does not need a non-existence result for the limit problem obtained by the usual blow-up procedure. This work is related to a previous one by Ruiz (2004) [9].