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Abstract
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We study the system involving fully nonlinear nonlocal operators:
We will prove the symmetry and monotonicity for positive solutions to the nonlinear
system in whole space by using the method of moving planes. To achieve it, a narrow
region principle and a decay at infinity are established. Further more, nonexistence of
positive solutions to the nonlinear system on a half space is derived. In addition, the
symmetry and monotonicity in whole space for positive solutions to a fully nonlinear
nonlocal system
can be derived.
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Keywords
fully nonlinear nonlocal operator, narrow region principle,
decay at infinity, method of moving planes
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Mathematical Subject Classification 2010
Primary: 35B06, 35B09, 35B50, 35B53
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Milestones
Received: 22 December 2017
Revised: 16 May 2018
Accepted: 24 June 2018
Published: 18 April 2019
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