On a Class of Nonlinear Elliptic Equations with General Growth in the Gradient

Abstract

In this paper, we prove an existence and uniqueness result for a class of Dirichlet boundary value problems whose model is −Δpu=β|∇u|q+c|u|p−2u+fin Ω,u=0on ∂Ω, where Ω is an open bounded subset of RN, N≥2, 1<p<N, Δpu is the so-called p-Laplace operator, and p−1<q<p. We assume that β is a positive constant, c and f are measurable functions belonging to suitable Lorentz spaces. Our approach is based on Schauder fixed point theorem.