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| Liouville Type Theorems for Nonlinear p-Laplacian Equation on Complete Noncompact Riemannian Manifolds* |
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Citation： |
Guangyue HUANG.Liouville Type Theorems for Nonlinear p-Laplacian Equation on Complete Noncompact Riemannian Manifolds*[J].Chinese Annals of Mathematics B,2023,44(3):379~390 |
| Page view： 702
Net amount： 532 |
Authors： |
Guangyue HUANG; |
Foundation： |
National Natural Science Foundation of China (No. 11971153) and Nanjing University of Aeronautics and Astronautics Research and Practice Innovation Program (No.xcxjh20220802). |
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| Abstract： |
In this paper, the authors study the gradient estimates for positive weak solutions to the following p-Laplacian equation ?pu + au σ = 0 on complete noncompact Riemannian manifold, where a, σ are two nonzero real constants with p 6 = 2. Using the gradient estimate, they can get the corresponding Liouville theorem.On the other hand, by virtue of the Poincar′e inequality, they also obtain a Liouville theorem under some integral conditions with respect to positive weak solutions. |
Keywords： |
p-Laplacian, Liouville theorem, Positive weak solution |
Classification： |
58J05, 58J35 |
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