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

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...

Full description

Saved in:
Bibliographic Details
Published inBulletin of mathematical sciences Vol. 14; no. 2
Main Authors Ahmed Mohammed, Antonio Vitolo
Format Journal Article
LanguageEnglish
Published World Scientific Publishing 01.08.2024
Subjects
comparison principles
maximum principles
Quasilinear elliptic operators
Online AccessGet full text
ISSN1664-3607
1664-3615
DOI10.1142/S166436072450005X

Cover

More Information
Summary: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.
ISSN:1664-3607
1664-3615
DOI:10.1142/S166436072450005X