Vol. 304, No. 1, 2020

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Symmetry and nonexistence of positive solutions for fractional Choquard equations

Pei Ma, Xudong Shang and Jihui Zhang

Vol. 304 (2020), No. 1, 143–167
Abstract

This paper is devoted to study the following Choquard equation:

()α2u = (|x|βn up)up1,u 0,x Rn,

where 0 < α,β < 2, 1 p < , and n 2. Using a direct method of moving planes, we prove the symmetry and nonexistence of positive solutions in the critical and subcritical cases respectively.

Keywords
The method of moving planes, fractional Laplacian, Choquard equation
Mathematical Subject Classification 2010
Primary: 35B06, 35B09, 35B50, 35B53, 35R11
Milestones
Received: 7 November 2018
Revised: 27 April 2019
Accepted: 25 May 2019
Published: 18 January 2020
Authors
Pei Ma
School of Mathematical Sciences
Nanjing Normal University;
College of Science
Nanjing Forestry University
Nanjing
China
Xudong Shang
Nanjing Normal University Taizhou College
Taizhou
China
Jihui Zhang
Jiangsu Key Laboratory for NSLSCS
School of Mathematical Sciences
Nanjing Normal University
Nanjing
China