Comparison principles for p-Laplace equations with lower order terms

Abstract

We prove comparison principles for quasilinear elliptic equations whose simplest model is (Formula presented.), where Δpu=div(|Du|p-2Du) is the p-Laplace operator with p> 2 , λ≥ 0 , H(x, ξ) : Ω × RN→ R is a Carathéodory function and Ω ⊂ RN is a bounded domain, N≥ 2. We collect several comparison results for weak sub- and super-solutions under different setting of assumptions and with possibly different methods. A strong comparison result is also proved for more regular solutions.