- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian Bull. Korean Math. Soc.Published online July 9, 2019 Fanqi Zeng School of Mathematics and Statistics, Xinyang Normal University Abstract : In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $$\Delta_{V}u+cu^{\alpha}=0,$$ where $c$, $\alpha$ are two real constants and $c\neq0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-Emery Ricci curvature bounded from below, which generalize some results of \cite{MHL2017}. Keywords : Gradient estimate, nonlinear elliptic equation, Bakry-Emery Ricci curvature MSC numbers : Primary 58J35, Secondary 35B45 Full-Text :