Symmetric properties for Choquard equations involving fully nonlinear nonlocal operator

Li Chen; Pengcheng Niu; Pengyan Wang

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Symmetric properties for Choquard equations involving fully nonlinear nonlocal operator

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arxiv 1905.06226 v1 pith:3X5YINQK submitted 2019-05-15 math.AP math-phmath.MP

Symmetric properties for Choquard equations involving fully nonlinear nonlocal operator

Pengyan Wang , Li Chen , Pengcheng Niu This is my paper

classification math.AP math-phmath.MP

keywords nonlocalchoquardfullyinvolvingnonlinearoperatorproblemssymmetric

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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.

Symmetric properties for Choquard equations involving fully nonlinear nonlocal operator

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