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In this paper, the positive solutions to Choquard equation involving fullynonlinear nonlocal operator are shown to be symmetric and monotone by using themoving plane method which has been introduced by Chen, Li and Li in 2015. Thekey ingredients are to obtain the "narrow region principle" and "decay atinfinity" for the corresponding problems. Similar ideas can be easily appliedto various nonlocal problems with more general nonlinearities.

Symmetric properties for Choquard equations involving fully nonlinear nonlocal operator