Comparison Principle for Elliptic Equations with Mixed Singular Nonlinearities

Abstract

We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by{−Δpu=fuγ+guqinΩ,u=0on∂Ω, where Ω is an open bounded subset of ℝN where Ω is an open bounded subset of ℝN, Δpu := ÷(|∇u|p− 2∇u) is the usual p-Laplacian operator, γ ≥ 0 and 0 ≤ q ≤ p − 1; f and g are nonnegative functions belonging to suitable Lebesgue spaces.