Radial symmetry for a generalized nonlinear fractional p-Laplacian problem
Articles
Wenwen Hou
Shanxi Normal University
https://orcid.org/0000-0002-0180-6490
Lihong Zhang
Shanxi Normal University
https://orcid.org/0000-0002-3144-2237
Ravi P. Agarwal
Texas A&M University
Guotao Wang
King Abdulaziz University
https://orcid.org/0000-0001-7197-8581
Published 2021-03-01
https://doi.org/10.15388/namc.2021.26.22358
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Keywords

generalized fractional p-Laplacian
method of moving planes
negative powers
radial symmetry and monotonicity

How to Cite

Hou W., Zhang L., Agarwal R. P. and Wang G. (2021) “Radial symmetry for a generalized nonlinear fractional p-Laplacian problem”, Nonlinear Analysis: Modelling and Control, 26(2), pp. 349-362. doi: 10.15388/namc.2021.26.22358.

Abstract

This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p-Laplacian, we study the monotonicity and radial symmetry of positive solutions of a generalized fractional p-Laplacian equation with negative power. In addition, a similar conclusion is also given for a generalized Hénon-type nonlinear fractional p-Laplacian equation.

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