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A direct method of moving planes for the fractional p-Laplacian system with negative powers

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Abstract

In this paper, we establish the direct method of moving planes for the fractional p-Laplacian system with negative powers. The key theorems are decay at infinity and a boundary estimate in the direct method of moving planes. Moreover, we apply the direct method of moving planes to obtain the radial symmetry and monotonicity of the positive solutions for the fractional p-Laplacian system with negative powers in the whole space. We also give one special case.

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Acknowledgements

The work was partially supported by NSFC(No.11271166). The authors would like to thank the reviewers for their helps and patience in improving this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Minghui Qie, Zhongxue Lü & Xin Zhang

Authors
  1. Minghui Qie
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  2. Zhongxue Lü
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  3. Xin Zhang
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Corresponding author

Correspondence to Zhongxue Lü.

Additional information

Communicated by K Sandeep.

The work was partially supported by NSFC (No.11271166), sponsored by Qing Lan Project.

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Qie, M., Lü, Z. & Zhang, X. A direct method of moving planes for the fractional p-Laplacian system with negative powers. Indian J Pure Appl Math 54, 344–358 (2023). https://doi.org/10.1007/s13226-022-00257-2

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