Symmetry and monotonicity of positive solutions for a system involving fractional p&q-Laplacian in a ball

Abstract

In this paper, we study a nonlinear system involving the fractional p&q-Laplacian in the unit ball {(−Δ)ps1u(x)+(−Δ)qs2u(x)=u(x)(v(x))β,x∈B1(0),(−Δ)ps1v(x)+(−Δ)qs2v(x)=v(x)(u(x))α,x∈B1(0),u=v=0,x∈Rn∖B1(0), where 0<s1, s2<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.

Topics & Concepts