Electron. J. Differential Equations, Vol. 2017 (2017), No. 258, pp. 1-11.

Liouville theorem and gradient estimates for nonlinear elliptic equations on Riemannian manifolds

Wen Wang, Hui Zhou, Xinquan Zhang

Abstract:
In this article we study a nonlinear elliptic equation by using the maximum principle and cutoff functions, We establish related gradient estimates, the Liouville theorem, and the Harnack inequality.

Submitted October 28, 2016. Published October 16, 2017.
Math Subject Classifications: 58J35, 35K05, 53C21.
Key Words: Gradient estimate; nonlinear elliptic equation; Liouville theorem; Harnack inequality.

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Wen Wang
School of Mathematics and Statistics
Hefei Normal University
Hefei 230601, China
email: wwen2014@mail.ustc.edu.cn
  Hui Zhou
School of Mathematics and Statistics
Hefei Normal University
Hefei 230601, China
email: zhouhui0309@126.com
  Xinquan Zhang
School of Mathematics and Statistics
Hefei Normal University
Hefei 230601, China
email: 285171107@qq.com

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