# Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms

@article{Chang2022LiouvilletypeTA,
title={Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms},
author={Caihong Chang and Bei Hu and Zhengce Zhang},
journal={Nonlinear Analysis},
year={2022}
}
• Published 17 August 2020
• Mathematics
• Nonlinear Analysis
2 Citations

### On the Liouville property for fully nonlinear equations with superlinear first-order terms

• Mathematics
• 2021
We consider in this note one-side Liouville properties for viscosity solutions of various fully nonlinear uniformly elliptic inequalities, whose prototype is F (x,Du) ≥ Hi(x, u,Du) in R , where Hi

### A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms

• Mathematics
• 2022
. In this article we study local and global properties of positive solutions of − ∆ m u = | u | p − 1 u + M |∇ u | q in a domain Ω of R N , with m > 1, p, q > 0 and M ∈ R . Following some ideas used

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Abstract We consider the elliptic quasilinear equation -Δm⁢u=up⁢|∇⁡u|q{-\Delta_{m}u=u^{p}\lvert\nabla u\rvert^{q}} in ℝN{\mathbb{R}^{N}}, q≥m{q\geq m} and p>0{p>0}, 1<m<N{1<m<N}. Our main result is a