Symmetric results of a Hénon type elliptic equation

Abstract

In this paper, we study the following weighted elliptic system −Δu+u=λ1|x|αu3+μ|x|βuv2,x∈B,−Δv+v=λ2|x|αv3+μ|x|βu2v,x∈B,u,v>0,x∈B,u=v=0,x∈∂B,where B⊂RN(N=2,3) is the unit ball centered at the origin, λ1,λ2>0, μ>0, β>0, α>0. By virtue of variational approaches and rescaling methods, the system has a nontrivial ground state solution with α>β>0, moreover, by reduction methods, the ground state solution is radial symmetry if β>0 small enough.