Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation

摘要

In this paper,we consider the following nonlinear elliptic equation △fu+huα =0on the complete smooth metric space (Rn,g0,e-fdvg0),where g0 is the Euclidean metric on Rn and f =|x|2/4.We prove gradient estimates and Liouville-Type theorems for positive solutions of the above equation.