TY - JOUR
T1 - Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation
AU - Chaona , Zhu
JO - Journal of Partial Differential Equations
VL - 3
SP - 237
EP - 251
PY - 2018
DA - 2018/09
SN - 31
DO - http://doi.org/10.4208/jpde.v31.n3.4
UR - https://global-sci.org/intro/article_detail/jpde/12707.html
KW - Gradient estimate
KW - Liouville-Type theorem
KW - shrinking gradient Ricci soliton.
AB - <p>In this paper, we consider the following nonlinear elliptic equation △_f^u+hu^α=0 on the complete smooth metric space (R<sup>n</sup>, g<sub>0</sub>, e −f dv<sub>g</sub><sub>0</sub>), where g<sub>0</sub>&nbsp;is the Euclidean metric on R<sup>n</sup>&nbsp;and f = |x|<sup>2</sup>/4. We prove gradient estimates and Liouville-Type theorems for positive solutions of the above equation.</p>