# American Institute of Mathematical Sciences

October  2018, 38(10): 5339-5349. doi: 10.3934/dcds.2018235

## Direct method of moving planes for logarithmic Laplacian system in bounded domains

 School of Mathematics and Physics, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District Beijing 100083, China

* Corresponding author: Baiyu Liu

Received  May 2018 Revised  May 2018 Published  July 2018

Fund Project: The author is supported by the National Natural Science Foundation of China (No.11671031) and the Fundamental Research Funds for the Central Universities FRF-BR-17-013A

Chen, Li and Li [Adv. Math., 308(2017), pp. 404-437] developed a direct method of moving planes for the fractional Laplacian. In this paper, we extend their method to the logarithmic Laplacian. We consider both the logarithmic equation and the system. To carry out the method, we establish two kinds of narrow region principle for the equation and the system separately. Then using these narrow region principles, we give the radial symmetry results for the solutions to semi-linear logarithmic Laplacian equations and systems on the ball.

Citation: Baiyu Liu. Direct method of moving planes for logarithmic Laplacian system in bounded domains. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 5339-5349. doi: 10.3934/dcds.2018235
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