Symmetry and classification of solutions to an integral equation of the Choquard type
Symmetry and classification of solutions to an integral equation of the Choquard type
Source title:
Comptes Rendus Mathematique, 357(11-12): 878-888,
2019
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
We study the integral equation
where and
. We prove that all positive
solutions to the equation are radially symmetric and monotone decreasing about some point, and we classify all such solutions when
. As a consequence, we derive similar results for positive
solutions to the higher-fractional-order Choquard-type equation