Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian

Lihong Zhang; Wenwen Hou; Bashir Ahmad; Guotao Wang

doi:10.3934/dcdss.2020445

Article Contents

2021, Volume 14, Issue 10: 3851-3863. Doi: 10.3934/dcdss.2020445

This issue Previous Article On the observability of conformable linear time-invariant control systems Next Article

Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian

a.
School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China
b.
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

^* Corresponding author: Bashir Ahmad
^* Corresponding author: Bashir Ahmad

Received: April 30, 2020

Revised: June 30, 2020

Early access: November 2020

Published: October 2021

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Abstract

In this paper, we investigate radial symmetry and monotonicity of positive solutions to a logarithmic Choquard equation involving a generalized nonlinear tempered fractional $ p $-Laplacian operator by applying the direct method of moving planes. We first introduce a new kind of tempered fractional $ p $-Laplacian $ (-\Delta-\lambda_{f})_{p}^{s} $ based on tempered fractional Laplacian $ (\Delta+\lambda)^{\beta/2} $, which was originally defined in [3] by Deng et.al [Boundary problems for the fractional and tempered fractional operators, Multiscale Model. Simul., 16(1)(2018), 125-149]. Then we discuss the decay of solutions at infinity and narrow region principle, which play a key role in obtaining the main result by the process of moving planes.

Keywords:

Generalized tempered fractional $ p $-Laplacian,
direct method of moving planes,
Choquard equations,
logarithmic nonlinearity,
radial symmetry and monotonicity.

Mathematics Subject Classification: 35A01, 35A30, 35B09.

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References

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