Symmetry and monotonicity of positive solutions for a system involving fractional p&q-Laplacian in a ball. Issue 4 (3rd April 2023) - Cao, Linfen; Fan, Linlin
Abstract : In this paper, we study a nonlinear system involving the fractional p&q-Laplacian in the unit ball 1 { ( − Δ ) p s 1 u ( x ) + ( − Δ ) q s 2 u ( x ) = u ( x ) ( v ( x ) ) β, x ∈ B 1 ( 0 ), ( − Δ ) p s 1 v ( x ) + ( − Δ ) q s 2 v ( x ) = v ( x ) ( u ( x ) ) α, x ∈ B 1 ( 0 ), u = v = 0, x ∈ R n ∖ B 1 ( 0 ), where 0 < s 1, s 2 < 1, p, q >2, α, β > 1 . By using the direct method of moving planes, we prove that the positive solutions ( u, v ) of the system must be radially symmetric and monotone decreasing about the origin.