Symmetry of Positive Solutions to Choquard Type Equations Involving the Fractional p-Laplacian
Symmetry of Positive Solutions to Choquard Type Equations Involving the Fractional p-Laplacian
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
where 0 < s < 1, 0 < α < n, p ≥ 2, q > 1, r > 0, a ≥ 0 and 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.