一类非线性p-Laplace方程的Liouville定理  

Liouville Theorems for a Nonlinear p-Laplace Equation

作　　者：蒋群群 王林峰[1] JIANG Qunqun;WANG Linfeng(School of Sciences,Nantong University,Nantong Jiangsu 226019,China)

机构地区：[1]南通大学理学院,江苏南通226019

出　　处：《广西师范大学学报（自然科学版）》2022年第2期116-124,共9页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11771223)。

摘　　要：在带有适当曲率条件的完备流形上研究非线性p-Laplace方程Δ_(p)u+au^(p-1)ln u+λu^(p-1)=0,式中a、λ和p>1为给定常数。通过考虑几何量沿p-Laplace方程的演化,在Ricci曲率有下界的紧致流形上建立上述方程的微分不等式。借助截断函数及Hessian比较定理,在截面曲率有下界的非紧流形上也建立类似不等式。作为应用得到了Liouville定理。In this paper the nonlinear p-Laplace equationΔ_(p)u+au^(p-1)ln u+λu^(p-1)=0 is studied on complete manifolds with some suitable curvature condition,where a,λand 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.

关 键 词：微分不等式 非线性 P-LAPLACE方程 LIOUVILLE定理 Ricci孤立子 

分 类 号：O186.1[理学—数学]