# 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} }

## 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 equation -Δu=uq|∇u|p{-\Delta u=u^{q}|\nabla u|^{p}} in ℝn{\mathbb{R}^{n}} for any p>2{p>2} and q>0{q>0}. We prove a Liouville-type theorem, which asserts that any…

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In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation $${u_t} - div\left( {{{\left| {\nabla u} \right|}^{p - 2}}\nabla u} \right) = - {\left| u…

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### Liouville Results and Asymptotics of Solutions of a Quasilinear Elliptic Equation with Supercritical Source Gradient Term

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- 2020

Abstract We consider the elliptic quasilinear equation -Δmu=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…