Bulletin of Mathematical Sciences (Aug 2024)
The effects of nonlinear perturbation terms on comparison principles for the -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: −Δpu + H(u,Du) = 0,x ∈ Ω, 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 Δpu = f(u) + g(u)|Du|q,x ∈ Ω, where [Formula: see text] are non-decreasing and [Formula: see text]. Our results either improve or complement those that appear in the literature.
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