In this paper, we investigate various comparison principles for quasilinear elliptic equations of p-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: −Δ_p u+H(u,Du)=0, x∈Ω, where Δ_p u := div(|Du|^(p−2)Du) is the p-Laplace operator with p > 1, and H is a continuous function that satisfies a structure condition. Many of these results lead to comparison principles for the model equations Δ_p u = f(u) + g(u)|Du|^q, x ∈ Ω, where f,g ∈ C0(\R,\R) are non-decreasing and q > 0. Our results either improve or complement those that appear in the literature.
The effects of nonlinear perturbation terms on comparison principles for the p-Laplacian
Ahmed Mohammed;Antonio Vitolo
2024-01-01
Abstract
In this paper, we investigate various comparison principles for quasilinear elliptic equations of p-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: −Δ_p u+H(u,Du)=0, x∈Ω, where Δ_p u := div(|Du|^(p−2)Du) is the p-Laplace operator with p > 1, and H is a continuous function that satisfies a structure condition. Many of these results lead to comparison principles for the model equations Δ_p u = f(u) + g(u)|Du|^q, x ∈ Ω, where f,g ∈ C0(\R,\R) are non-decreasing and q > 0. Our results either improve or complement those that appear in the literature.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
