A priori estimates for elliptic equations with gradient dependent term and zero order term

In this paper we prove an existence result for “solution obtained as limit of approximations” to a class of Dirichlet boundary value problems whose prototype is {−Δpu=β(1+|∇u|)q+c(x)|u|p−2u+finΩu=0on∂Ω, where Ω is a bounded open subset of RN, N≥2, 1<2, Δpu=div(|∇u|p−2∇u), [Formula presented], β is a positive constant, c with c≥0, c≠0 and f are measurable functions satisfying suitable summability conditions depending on q. We further assume smallness assumptions on β, c and f. Our approach is based on Schauder's fixed point theorem. Similar results can be proved also for 2≤p