Open AccessRadial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian
Author(s) -
Lihong Zhang,
Wenwen Hou,
Bashir Ahmad,
Guotao Wang
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2020445
Subject(s) - fractional laplacian , mathematics , operator (biology) , laplace operator , symmetry (geometry) , monotonic function , combinatorics , logarithm , mathematical analysis , geometry , biochemistry , chemistry , repressor , transcription factor , gene
In this paper, we investigate radial symmetry and monotonicity of positive solutions to a logarithmic Choquard equation involving a generalized nonlinear tempered fractional \begin{document}$ p $\end{document} -Laplacian operator by applying the direct method of moving planes. We first introduce a new kind of tempered fractional \begin{document}$ p $\end{document} -Laplacian \begin{document}$ (-\Delta-\lambda_{f})_{p}^{s} $\end{document} based on tempered fractional Laplacian \begin{document}$ (\Delta+\lambda)^{\beta/2} $\end{document} , 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.