# 学术讲座 Lecture

## 【21.1.15 10:30-11:30】学术报告---孙玉华教授

2021-01-12 11:38:09 来源：学术报告---孙玉华教授 点击： 收藏本文

We investigate the nonexistence and existence of nontrivial positive solutions to $\Delta_m u+u^p|\nabla u|^q\leq0$ on $M$, where $m>1$, $M$ is a noncompact geodesically complete manifold, and $(p,q)\in \mathbb{R}^2$. According to classification of $(p, q)$, we establish sharp volume growth conditions to present Liouville's theorems for the above quasilinear differential inequalities. Moreover, the results are completely new for $(p, q)$ of negative power, even in the Euclidean space.