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

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 (− Δ − λ_ƒ)^s_p based on tempered fractional Laplacian (Δ + λ)^β/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. [ABSTRACT FROM AUTHOR]