ON A CLASS OF NONLINEAR ELLIPTIC EQUATIONS WITH LOWER ORDER TERMS

In this paper we prove an existence result for weak solutions to a class of Dirichlet boundary value problems whose prototype is −∆pu = β|∇u|^q + c(x)|u|^{p−2}u + f in Ω u = 0 on ∂Ω, is a bounded open subset of R^N,N ≥2, ∆_pu=div (|∇u|^{p−2}∇u ), is the so-called p−Laplace operator, 1 < p < N , p − 1 < q ≤ p − 1 + p . We assume that β is a positive constant, c ∈ L^N (Ω), with c ≥ 0 and f ∈ L(p^*)′(Ω). We further assume smallness assumptions on c and f. Our approach is based on Schauder’s fixed point theorem.