The effects of nonlinear perturbation terms on comparison principles for the p-Laplacian

Abstract

In this paper, we investigate various comparison principles for quasilinear elliptic equations of [Formula: see text]-Laplace type with lower-order terms that depend on the solution and its gradient. More specifically, we study comparison principles for equations of the following form: [Formula: see text] where [Formula: see text] is the [Formula: see text]-Laplace operator with [Formula: see text], and [Formula: see text] is a continuous function that satisfies a structure condition. Many of these results lead to comparison principles for the model equations [Formula: see text] where [Formula: see text] are non-decreasing and [Formula: see text]. Our results either improve or complement those that appear in the literature.