Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (2): 116-124.doi: 10.16088/j.issn.1001-6600.2021052401

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Liouville Theorems for a Nonlinear p-Laplace Equation

JIANG Qunqun, WANG Linfeng*   

  1. School of Sciences, Nantong University, Nantong Jiangsu 226019, China
  • Received:2021-05-24 Revised:2021-07-08 Published:2022-05-31

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Abstract: In this paper the nonlinear p-Laplace equation Δpu+aup-1lnu+λup-1=0 is studied on complete manifolds with some suitable curvature condition, where a, λ and p>1 are some given constants. Differential inequalities for the p-Laplace equation on compact manifolds with Ricci curvature bounded from below are established, based on the evolution of the geometric quantity along the p-Laplace equation. Similar inequalities can also be established on a noncompact manifold whose sectional curvature is bounded from below, based on the skills of cut off function and the Hessian comparison theorem. As an application, Liouville theorems are obtained.

Key words: differential inequality, nonlinear, p-Laplace equation, Liouville theorem, Ricci soliton

CLC Number: 

  • O186.1
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