Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation (Journal of Partial Differential Equations, 2018)
In this paper, we consider the following nonlinear elliptic equation △_f^u+hu^α=0 on the complete smooth metric space (Rn, g0, e −f dvg0), 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.
Keywords: Gradient estimate; Liouville-Type theorem; shrinking gradient Ricci soliton.