Symmetry and monotonicity of positive solutions for a system involving fractional p&q-Laplacian in a ball. Issue 4 (3rd April 2023)

• Record Type: Journal Article
• Authors: Cao, Linfen; Fan, Linlin
• Is Part Of: Complex variables and elliptic equations. Volume 68:Issue 4(2023)
• Page Start: 667
• Page End: 679
• Publication Date: 2023-04-03
• Subjects: Method of moving planes -- fractional p&q-Laplacian -- radial symmetry -- monotonicity; Primary: 35R11 -- Secondary: 35J92; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.2009819
• Languages: English
• ISSNs: 1747-6933

Abstract

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.