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

  • * Corresponding author: Bashir Ahmad

    * Corresponding author: Bashir Ahmad 
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  • 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.

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


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