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| 摘要: |
| 设（Mn，g）是一个n维非紧的完备黎曼流行.本文考虑有正解的非线性椭圆方程△fu+au log u=0的刘维尔型定理，其中a是一个非零常数.利用Bochner公式和极大值原理，获得了以上方程在Bakry-Emery里奇曲率有下界时正解的Li-Yau型梯度估计和某些有关的刘维尔理论，推广了文献[7]的结果. |
| 关键词: 梯度估计 非线性椭圆方程 刘维尔型定理 极大值原理 |
| DOI： |
| 分类号:O175.25;O175.29 |
| 基金项目:Supported by the National Natural Science Foundation of China (11201131); Hubei Key Laboratory of Applied Mathematics (Hubei University). |
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| LIOUVILLE TYPE THEOREMS FOR A NONLINEAR ELLIPTIC EQUATION |
|
XIANG Ni,CHEN Yong
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| Abstract: |
| Let (Mn, g) be an n-dimensional complete noncompact Riemannian manifold. In this paper, we consider the Liouville type theorems for positive solutions to the following nonlinear elliptic equation:△fu + au log u=0, where a is a nonzero constant. By applying Bochner formula and the maximum principle, we obtain local gradient estimates of the Li-Yau type for positive solutions of the above equation on Riemannian manifolds with Bakry-Emery Ricci curvature bounded from below and some relevant Liouville type theorems, which improve some results of[7]. |
| Key words: gradient estimate nonlinear elliptic equation Liouville-type theorem maximum principle |
