Liouville Type Theorems for Nonlinear p-Laplacian Equation on Complete Noncompact Riemannian Manifolds*

被引：2

作者：

Huang, Guangyue ^{[1
]}

Zhao, Liang ^{[2
]}

机构：

[1] Henan Normal Univ, Dept Math, Xinxiang 453007, Henan, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Sch Math, Nanjing 210016, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2023年 / 44卷 / 03期

基金：

中国国家自然科学基金;

关键词：

p-Laplacian; Liouville theorem; Positive weak solution; ELLIPTIC EQUATION; GRADIENT;

D O I：

10.1007/s11401-023-0021-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the authors study the gradient estimates for positive weak solutions to the following p-Laplacian equation?(p)u + au(s) = 0on complete noncompact Riemannian manifold, where a, s are two nonzero real constants with p? 2. Using the gradient estimate, they can get the corresponding Liouville theorem. On the other hand, by virtue of the Poincare'inequality, they also obtain a Liouville theorem under some integral conditions with respect to positive weak solutions.

引用

页码：379 / 390

页数：12

共 50 条

[1] Liouville Type Theorems for Nonlinear p-Laplacian Equation on Complete Noncompact Riemannian Manifolds
Guangyue Huang
Liang Zhao
[J]. Chinese Annals of Mathematics, Series B, 2023, 44 : 379 - 390
[2] Liouville Type Theorems for Nonlinear p-Laplacian Equation on Complete Noncompact Riemannian Manifolds
Guangyue HUANG
Liang ZHAO
[J]. Chinese Annals of Mathematics,Series B, 2023, (03) : 379 - 390
[3] On some Liouville theorems on noncompact Riemannian manifolds
Losev, AG
[J]. SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (01) : 74 - 80
[4] Bounds for eigenfunctions of the Neumann p-Laplacian on noncompact Riemannian manifolds
Barletta, Giuseppina
Cianchi, Andrea
Maz'ya, Vladimir
[J]. ADVANCES IN CALCULUS OF VARIATIONS, 2024, 17 (02) : 319 - 352
[5] On some Liouville theorems on noncompact Riemannian manifolds
A. G. Losev
[J]. Siberian Mathematical Journal, 1998, 39 : 74 - 80
[6] Gradient estimates and Liouville theorems for nonlinear parabolic equations on noncompact Riemannian manifolds
Zhu, Xiaobao
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (15) : 5141 - 5146
[7] On the p-Laplacian Lichnerowicz equation on compact Riemannian manifolds
Nanbo Chen
Xiaochun Liu
[J]. Science China Mathematics, 2021, 64 (10) : 2249 - 2274
[8] On the p-Laplacian Lichnerowicz equation on compact Riemannian manifolds
Nanbo Chen
Xiaochun Liu
[J]. Science China Mathematics, 2021, 64 : 2249 - 2274
[9] Gradient bounds and Liouville's type theorems for the Poisson equation on complete Riemannian manifolds
Ratto, A
Rigoli, M
[J]. TOHOKU MATHEMATICAL JOURNAL, 1995, 47 (04) : 509 - 519
[10] Liouville Type Theorems in the Theory of Mappings of Complete Riemannian Manifolds
Aleksandrova I.A.
Mikeš J.
Stepanov S.E.
Tsyganok I.I.
[J]. Journal of Mathematical Sciences, 2017, 221 (6) : 737 - 744

← 1 2 3 4 5 →