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Abstract
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This paper is devoted to study the following Choquard equation:
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where
,
, and
.
Using a direct method of moving planes, we prove the symmetry and nonexistence of
positive solutions in the critical and subcritical cases respectively.
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Keywords
The method of moving planes, fractional Laplacian, Choquard
equation
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Mathematical Subject Classification 2010
Primary: 35B06, 35B09, 35B50, 35B53, 35R11
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Milestones
Received: 7 November 2018
Revised: 27 April 2019
Accepted: 25 May 2019
Published: 18 January 2020
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