Symmetric properties for Choquard equations involving fully nonlinear nonlocal operator

In this paper, the positive solutions to Choquard equation involving fully nonlinear nonlocal operator are shown to be symmetric and monotone by using the moving plane method which has been introduced by Chen, Li and Li in 2015. The key ingredients are to obtain the “narrow region principle” and “decay at infinity” for the corresponding problems. Similar ideas can be easily applied to various nonlocal problems with more general nonlinearities.