Symmetric results of a Henon type elliptic equation

In this paper, we study the following weighted elliptic system {-Delta u + u = lambda 1 vertical bar x vertical bar(alpha)u(3) + mu vertical bar x vertical bar(beta)uv(2), x is an element of B, -Delta v + v = lambda(2)vertical bar x vertical bar(alpha)v(3) + mu vertical bar x vertical bar(beta)u(2)v, x is an element of B, where B C R-N(N = 2,3) is the unit ball centered at the origin, lambda(1), lambda(2) > 0, mu > 0, beta > 0, alpha > 0. By virtue of variational approaches and resealing methods, the system has a nontrivial ground state solution with alpha > beta > 0, moreover, by reduction methods, the ground state solution is radial symmetry if beta > 0 small enough. (C) 2019 Elsevier Ltd. All rights reserved.