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Symmetry of Positive Solutions to Choquard Type Equations Involving the Fractional p-Laplacian

Authors: 

Phuong Le

Source title: 
Acta Applicandae Mathematicae, 170: 387-398, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

We study symmetric properties of positive solutions to the Choquard type equation

a

where 0 < s < 10 < α < np ≥ 2, q > 1, r > 0a ≥ 0 and a is the fractional p-Laplacian. Via a direct method of moving planes, we prove that every positive solution u which has an appropriate decay property must be radially symmetric and monotone decreasing about some point, which is the origin if a > 0.