Radial symmetry of solutions for some integral systems of Wolff type

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Super Polyharmonic Property of Solutions for PDE Systems and Its Applications (2011, unknown): “(ii) the fully nonlinear integral systems involving Wolff potentials [14]: { u(x) = Wβ,γ(v )(x), x ∈ R; v(x) = Wβ,γ(u )(x), x ∈ R; (6)”
Liouville type theorems for integral equations and integral systems (2013, unknown): “in [9] and [10] and then used widely in [6,8,17–19,23–26].”
The existence of extremal functions for discrete Sobolev inequalities on lattice graphs (2021, background): “2) as follows, see [6, 7, 8, 9, 10, 11, 12] for continuous setting and [13, 29] for discrete setting.”
Sharp criteria of Liouville type for some nonlinear systems (2013, background): “3) { u(x) = Wβ,γ(v )(x) v(x) = Wβ,γ(u )(x), Chen and Li [8] proved the radial symmetry for the integrable solutions.”