一类非线性椭圆方程的刘维尔型定理（英文）  

LIOUVILLE TYPE THEOREMS FOR A NONLINEAR ELLIPTIC EQUATION

作　　者：向妮[1] 陈勇[1] 

机构地区：[1]湖北大学数学与统计学院,湖北武汉430062

出　　处：《数学杂志》2017年第5期977-986,共10页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(11201131);Hubei Key Laboratory of Applied Mathematics(Hubei University)

摘　　要：设(M^n,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.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 fol｜owing 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].

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 

分 类 号：O175.25[理学—数学] O175.29[理学—基础数学]