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Symmetry of solutions for a fractional p-Laplacian equation of Choquard type


Phuong Le

Source title: 
International Journal of Mathematics, 2050026, 14 pages, 2020 (ISI)
Academic year of acceptance: 

Let a and u be a positive solution of the equation


We prove that if u satisfies some decay assumption at infinity, then u must be radially symmetric and monotone decreasing about some point in a. Instead of using equivalent fractional systems, we exploit a generalized direct method of moving planes for fractional p-Laplacian equations with nonlocal nonlinearities. This new approach enables us to cover the full range 0<α<n in our results.