标题： 完备黎曼流形上一类椭圆方程的Liouville定理 显示英文标题

标题： Liouville theorem for one kind of elliptic equations on complete Riemannian manifold

摘要： 我们使用最大值原理来证明在具有非负Ricci张量的完备黎曼流形上方程$\Delta U + b\cdot \nabla U + h U^{\alpha} = 0, U \geq 0, 0 < \alpha < \frac{n + 2}{n - 2}$的Liouville定理，这改进了Gidas-Spruck和Catino-Monticelli的结果。 我们备注这是第二版，所有的结果都来自第一版。 在我们将第一版预印本发布到arXiv两个月后，我们发现Zhihao Lu已经在他之前发布了论文arXiv:2308.14764，他的部分结果与我们的结果一致。 因此，在删除这些部分并添加更多参考文献和细节后，我们将在arXiv上发布这一第二版。 显示英文摘要

摘要： We use maximum principle to prove the Liouville theorem of the equation $\Delta U + b\cdot \nabla U + h U^{\alpha} = 0, U \geq 0, 0 < \alpha < \frac{n + 2}{n - 2}$ on the complete Riemannian manifold with non-negative Ricci tensor, which improve the result of Gidas-Spruck and Catino-Monticelli. We remark that this is the second version and all of the results come from the first version. Two months after we posted version 1 of this preprint on arXiv, we found Zhihao Lu has already posted a paper arXiv:2308.14764 before us and part of his result coincides with ours. So after deleting these parts and adding more reference and details, we post this second version on arXiv.