Solutions of fully nonlinear nonlocal systems.

In this paper we consider the system involving fully nonlinear nonlocal operators: { F α ( u ( x ) ) = C n , α P V ∫ R n G ( u ( x ) − u ( y ) ) | x − y | n + α d y = f ( v ( x ) ) , F β ( v ( x ) ) = C n , β P V ∫ R n G ( v ( x ) − v ( y ) ) | x − y | n + β d y = g ( u ( x ) ) . For carrying on the method of moving planes, a narrow region principle and a decay at infinity are established. Then we prove the radial symmetry and monotonicity for positive solutions to the nonlinear system in the whole space. Furthermore, non-existence of positive solutions to the nonlinear system on a half space is derived. [ABSTRACT FROM AUTHOR]